Control over youth justice and policing should be devolved to Wales, a report into assembly powers has recommended.
The Silk Commission said other parts of the justice system could follow in future, subject to a review.
Large-scale energy projects should also be the responsibility of the Welsh government, and the number of assembly members increased.
The report was broadly welcomed across the political spectrum but Plaid Cymru said it fell short of "real progress".
Prime Minister David Cameron said the report had proposed a "new course for the future", while Welsh Secretary David Jones said it raised "important questions about the future governance of Wales".
Set up by the UK coalition government, this is the commission's second report.
The first paved the way towards new tax and borrowing powers for the Welsh government.
After a year-long review, the commission found:
- The current settlement was too complex for people to understand or to find out where power lies
- There was a need for governments and institutions to work together better
- There was broad support for devolving more powers
The report proposed a "realistic" 10-year timetable - including legislation after the next general election - and 61 recommendations to create a "clear, well-founded devolution settlement".
The Welsh government's responsibility for energy generation should increase from a limit of 50MW schemes to schemes of up to 350MW.
The report also recommended changing the way the assembly's powers are defined.
A reserved powers model, such as the one in Scotland, would list the powers that are not devolved, rather than being a list of powers which are under the assembly's control.
Supporters of the move said it would clarify the assembly's powers.
There was also a recommendation for an increase in the number of AMs.
The commission stopped short of specifying a figure but said an increase from the current 60 to 80 "would balance enhanced scrutiny capacity with restraint in public spending".
Commission chairman Paul Silk said: "At a time when constitutional issues are high on the agenda in the United Kingdom, we have agreed recommendations that will provide a stable and well-founded devolution settlement fit for the future.
"It will give Wales a lasting settlement that allow political decisions to be made in a democratic and accountable manner.
"Through a phased 10-year programme of reform, it will create a stronger Welsh democracy and bring Wales more in line with the other devolved countries of the UK."
Among other recommendations are the devolution of more powers over rail and ports, and a call for the assembly to have law-making powers over water policy in Wales.
The commission said the regulation of broadcasting should stay in Westminster. However, the report recommended creating a devolved body within the BBC Trust and said the UK government funding for S4C should move to the Welsh government.
It found there was no case to hand powers back to Westminster from Cardiff Bay.
On policing, the report said most evidence submitted supported its devolution as a way to bring it in line with other public services.
But it said responsibilities for the the National Crime Agency should not be devolved, neither should powers to do with arresting, interrogating and charging suspects, unless criminal law was also devolved.
IMPLEMENTING THE CHANGES
A 10-year programme of reform in three phases is recommended to make devolution changes, with administrative recommendations in place before the next general election in 2015, and implementation of the review of changes to the justice system by 2025.
Policing should be devolved but powers relating to arrest, interrogation and charging suspects should not be unless criminal law was devolved, according to the commission.
It also said police pay should be devolved but not pensions.
Treatment and rehabilitation of youth offenders should be devolved.
There was also a "persuasive case" for devolving the prison service - and the two governments should carry out a feasibility study, said Mr Silk.
High Court divisions should sit in Wales on a regular basis and a High Court office for Wales should be established, the report added.
A review should be carried out within 10 years into the case for devolving legislative responsibility for the court service, sentencing, legal aid, the CPS and judiciary.
The commission recommended that a Welsh Criminal Justice Board should also be created.
The report said the size of the Welsh Assembly should be increased and its official name changed to Senedd.
A range of options should also be considered for increasing the capacity within the existing assembly, including greater flexibility on the number and size of committees and more research staff.
The Welsh secretary's right to participate in assembly proceedings should be removed, and UK minister's power to prevent assembly bills going forward for Royal Assent should be aligned with those in Scotland.
Development of ports, the Wales and Border rail franchise, funding of Network Rail in Wales, speed and drink-drive limits, and bus and taxi regulation should all be devolved, said the commission.
Wales should also have a greater role in appointing rail franchises for cross-border rail services. The report added there should be close coordination on cross-border road routes.
The UK and Welsh governments should provide a clearer and better co-ordinated approach to employment and training policies, said the report.
It added that both governments needed to take account of each other's policies when developing economic strategies for Wales.
The report said the existing 'conferred powers' model should be replaced by a 'reserved powers' model, which means rather than saying which areas Wales has control over, it should list which ones it does not.
There should be a general transfer of pre-devolution powers to Welsh ministers, subject to necessary exceptions, it added.
Teachers' pay and conditions should be devolved but pensions should remain with the UK government, said Mr Silk.
A formal joint committee on higher education and research should be established to "ensure a coherent approach to policy and assess the impact of UK decisions on institutions in Wales".
BBC Wales education correspondent Arwyn Jones said teachers in Wales and England who are members of the NUT will strike on 26 March in the latest phase of the unions' ongoing campaign of industrial action over pay, pensions and working conditions.
They are unhappy with UK Education Secretary Michael Gove, but there is no agreement as to whether the system would be better run from Cardiff Bay.
There is no guarantee that the Welsh government would be any more generous than its UK counterpart. Schools in Wales receive less money than those in England, so some teachers worry the same could apply to them too.
Having said that, as both countries increasingly go their own way on education policies, others argue there is little point keeping the joint system.
NUT Cymru Secretary David Evans said: "This recommendation should be rejected by the Welsh government. Acceptance would undoubtedly lead to a position whereby pay rates would be driven down and the NUT could never agree to a situation where teachers in Wales could end up being paid less than colleagues in other areas of the UK for doing the same work.
"That is an issue previously recognised at the Senedd and there is no valid argument put forward in the commission's report that would justify any change of mind.
"Teachers' pay and conditions must be protected if we are to ensure that the best practitioners remain in our Welsh schools."
But the UCAC union warmly welcomed to the recommendation that teachers' pay and conditions should be devolved.
Elaine Edwards, UCAC's general secretary, said "At a time when education policies in Wales and England are diverging at an increasing rate, there's little point in preserving a joint system of pay and conditions.
"It's a power that's already devolved in Scotland and Northern Ireland, and we're extremely pleased the commission has made an unambiguous recommendation on the matter."
The commission recommended no change to the devolution settlement in relation to health, and said social security should remain with the UK government.
There should be "equitable" cross-border access for patients and a "strategic approach" to joint delivery of health services.
The report recommended that regulation should remain the responsibility of the UK government.
The BBC should have a devolved governance body to scrutinise output in Wales, it added, while the responsibility for funding the public expenditure element of S4C should be devolved to Wales. This amount is currently around £6.7m per year, while the bulk of S4C's annual funding (around £76m) has come from the BBC licence fee since April 2013.
It also says the BBC's National Trustee for Wales should be appointed by a formal agreement between the Welsh and UK governments, which would bring Wales in line with a process that already occurs with Scotland.
Similarly, the commission recommends that the appointment of members of S4C's governing body, the S4C Authority, by the UK government should require Welsh government agreement. This would formalise a process that already involves a degree of co-operation between ministers in Westminster and Cardiff Bay.
Elan Closs Stephens, BBC Trustee for Wales, said in statement: "We welcome this report's thoughtful contribution to the debate about broadcasting in Wales and we note its findings.
"The structure of BBC governance is a matter for the UK government; the trust is focused on delivering its responsibilities as set out under the current charter.
"As trustee for Wales I was appointed to ensure that the interests of Welsh licence fee payers are represented in the trust's collective decision making; the trust also benefits from the in-depth advice of the Audience Council Wales on the BBC's performance and any emerging issues of importance for audiences in Wales."
All energy projects which produce up to 350MW should be devolved, and the UK government should have to consult Wales on projects over that size, said the commission.
Wales should also get power over sewerage. Responsibility for marine conservation should be extended from inshore areas to offshore.
Local government elections should be devolved, the commission reported.
Prime Minister David Cameron said he was "proud of this government's record in delivering for Wales and bringing further devolution".
"The tax and borrowing powers we are devolving will give the Welsh Assembly and Welsh government additional means to help generate economic growth and today's report makes recommendations that propose a new course for the future," he said.
Welsh Secretary David Jones said: "This government has consistently reaffirmed its clear commitment to devolution, and we warmly welcome the commission's second report which sets out its recommendations for making devolution in Wales work better.
"The report raises crucially important questions about the future governance of Wales within the United Kingdom. Therefore, it is only right that we now take the time to consider in full each of the recommendations and their implications.
"We will consider implementing some of the changes the commission has recommended during this parliament. But there is insufficient time remaining in this parliament to implement any changes that require primary legislation.
"These will therefore be a matter for the next government and parliament, and for political parties to set out their proposals and intentions to the electorate ahead of the general election in 2015."
First Minister Carwyn Jones said the force of the report was "enhanced by the fact that the commission, with representatives from all four political parties among its membership, is unanimous in its recommendations".
"It now falls to the Welsh government, and to all political parties, to use the next few weeks to consider the commission's recommendations in detail. I will then be calling for a debate on the report in the assembly immediately after the Easter recess," he said.
"The Welsh government believes the new powers should be devolved to the assembly by 2020/21, as part of a wider reform of the UK constitution following the Scottish independence referendum.
"Devolution is the settled will of the people of Wales. I want the United Kingdom to flourish, and a devolved Wales to play a dynamic role in it. But for this to happen, the governance of the UK must adapt to the reality of its devolved democracy and the aspirations of its citizens.
"I hope that the commission's report will provide us with the foundation on which to build a blueprint for reform which can be supported by a cross-party consensus in the assembly.
"This will put us in the strongest possible position to work with the UK government to turn this vision into reality."
Welsh Liberal Democrat leader Kirsty Williams said: "In only a short space of time and against much resistance, Liberal Democrats in government have been the driving force in ensuring there is now real momentum behind the devolution process.
"We have a proud record of bringing decision making closer to the people of Wales and we will continue to fight for that to be the case."
Plaid Cymru parliamentary leader Elfyn Llwyd said the report fell short of signalling "real progress" on securing more meaningful powers for Wales.
"Having made great strides on the devolution journey in recent decades, it feels as if Wales is now sadly being dragged along at an agonisingly slow pace of progress," he said.
"Plaid Cymru believes that all decisions affecting the people of Wales should be made in Wales."
Welsh Conservative leader Andrew RT Davies said: "We welcome the publication of this report - the culmination of years of work by Paul Silk and the members of his commission.
"I pay tribute to the commendable work of the commission in drawing up two packages of recommendations intended to improve governance and democratic accountability in Wales.
"All political parties should study these recommendations in detail with the aim of achieving cross-party consensus on the way forward."
Presiding Officer of the National Assembly for Wales, Dame Rosemary Butler AM, said: "I welcome the package of recommendations from the Commission on Devolution, in particular the issue of more Assembly Members. More members means greater opportunity to develop the necessary expertise and knowledge required to robustly challenge government ministers on their proposals.
"I believe the package of recommendations provides a strong basis for the development of devolution in Wales, to strengthen democracy and accountability and, most importantly, for the assembly to better serve the people of Wales."
Steve Brooks, director of the Electoral Reform Society Cymru, said: "The commission's work, and in particular its push to ensure accountability and localism lay at the heart of its recommendations, are warmly welcome.
"The Electoral Reform Society is pleased that the commission recognises the wide body of evidence which highlights the urgent and critical need for more assembly members."
True Wales, which campaigned against extending the powers of the assembly, said it was "appalled at the extent of the radical changes" being proposed.
"During the 2011 referendum, Yes politicians and campaigners continually denied that the devolution of tax powers, criminal justice and policing, more AMs and a separate legal jurisdiction would follow a Yes vote," the group said in a statement.
"Two years on from referendum day, we have the extraordinary spectacle of a commission recommending all of those radical changes that we predicted would follow a Yes vote, as well as the reserved powers model."