BBC Wales political reporter Daniel Davies explains what happens now that the result of the referendum is known.
Welsh voters have gone with the opinion polls and given a resounding Yes to direct law-making powers.
Only one county - Monmouthshire - voted No.
Now the result has been announced, what happens next?
There is no change to the 20 policy fields that are devolved to the assembly. They include education and health.
Those fields stay the same. AMs will not be able to stray into new areas, such as taxation and policing.
What changes as a result of this referendum is that the assembly can pass laws in those 20 fields without having to refer to parliament first.
The Yes vote scraps a system that has existed since 2007 whereby the assembly is able to bid to Westminster for primary legislative powers on a case-by-case basis.
But the new system will not be introduced overnight.
The assembly will not acquire its powers instantly - it must complete a formal process to activate part 4 of the 2006 Government of Wales Act.
A commencement order needs to be approved by a simple majority of AMs. It is likely to happen before the assembly dissolves for May's elections.
Under the outgoing system, pieces of primary legislation in the assembly are called measures. The Yes vote means measures that are yet to complete their passage to the statue book are unaffected. Those passed by AMs before dissolution will go forward for Royal Assent as normal.
Once the commencement order is passed, legislation in Cardiff Bay will be called Bills and Acts, as in parliament.
Assembly acts will need the Queen's stamp of approval. Work is underway to design a Welsh Seal that will appear on future legislation.
The final design is a matter for Buckingham Palace, with advice taken from the College of Heraldry, among others.