They are opening in former office blocks and libraries and Grade II listed buildings, being set up in England by religious groups and groups behind existing academies as well as by some parents and teachers.
They include a Montessori school, schools where meditation and yoga are part of the timetable and private schools joining the state sector.
They are small in number compared with the total number of schools in England - the first 24 open this month - but they are bringing in changes and their impact could be big.
In future any new school being set up will probably be a free school.
Local authorities will no longer build schools themselves, so the free schools programme will be the gateway for "education providers" - including faith groups and those behind existing academy chains - to establish new schools.
Parents and teachers are also being encouraged to set up schools or lobby for them in what the government says should be a "community-led" programme.
Free schools were a key part of the Conservative election manifesto and they reflect dramatic structural changes to the way England's schools are set up and run.
There is a lot of controversy around the changes, with critics saying they will lead to the break-up of the state education system and that the free schools will draw money and pupils away from other schools.
Local accountability will be lost, they say, together with the role of councils in planning school places.
Liberal Democrat tension
Opponents also believe the changes open the door for businesses to play a bigger role in England's education system.
Deputy Prime Minister Nick Clegg attempted to put those fears at bay earlier this week when he ruled out allowing free schools to be run for profit.
There is tension between the coalition partners on the schools.
Mr Clegg's Liberal Democrats voted against free schools at last year's party conference, but the Conservative Education Secretary Michael Gove has in the past said he is "relaxed" about the idea of groups making profits from running schools, although the government has no plans to change the law to allow this.
The free schools are part of wider changes.
While the government wants new groups to come forward to set up schools, it also wants all good existing schools to become academies - and like the free schools, these will be funded directly by Westminster and be outside of local authority control.
That conversion process began soon after the general election, and figures out earlier this week showed that since this time last year, more than 1,000 schools have switched to become academies.
What are the other changes coming in with free schools?
Like academies, free schools have more freedom over the timetable and curriculum than other schools, and over the pay and conditions of staff. They are also free to hire teachers who are not qualified.
Some are advertising smaller class sizes - 24 or under - and Saturday morning sessions, while some have changed the usual pattern of school holidays.
At the E-ACT free school in Redbridge, east London, the summer holiday will be cut to four weeks.
The primary school is also offering breakfast and after-school care for pupils, running from 0800 to 1800.
Many other schools in England have also offered this kind of "wrap-around" care for some time, but E-ACT - one of the groups sponsoring new academies and free schools - says its sessions will be different in that they will include additional "learning and development classes" led by teachers.
It says the freedom to vary teachers' pay and conditions from those used across the general state school sector has enabled it to do that.
This freedom is another reason that teaching unions dislike the move towards free schools and academies, fearing national agreements will be tossed aside and their members' rights eroded.
However, the National Union of Teachers says that so far there have not been many complaints about this happening in the new schools.
The union's general secretary, Christine Blower, said: "We don't notice a big move away from pay and conditions. We have not had people coming forward to us saying 'they are not prepared to talk to us'.
"We have had some discussions with schools where they will stay roughly in line with pay and conditions."
In one case, Ms Blower said, a school had said it would only employ qualified teachers.
Another broad change the free schools usher in is in the variety of schools now being funded by the tax-payer.
For critics, like the other big classroom teachers' union the NASUWT, this means a "reckless experiment", in which children will suffer.
The key aims of the programme, the government says, are to improve standards of education in England, particularly for poorer pupils - and to give parents more choice.
It says half of the new free schools are in deprived parts of the country, although this has been disputed, with opponents saying they will mainly serve middle-class areas.
In some cases free schools have come about after academy chains (those behind existing academy schools) have identified a shortage of school places in an area and approached the local council to suggest it sets up a school there.
There are severe shortages of primary school places in London and the Midlands.
Hammersmith and Fulham Council in west London says its new primary free school - Ark Conway - came about because of a three-way partnership between the local authority, the Ark academy chain and parents.
Parent Emily Philips had approached the council with the idea of setting up a school in the north of the borough where she lives because she was worried that her daughter - who was then two - would not get a school place nearby.
She had spoken to other parents and gathered support for a new school a few years ago, "setting the wheels in motion".
The Ark group came along, she said, after the free school legislation came in and she began to felt the "overwhelming reality" of what would be involved in setting up a new school.
In retrospect, she feels she was "naive" to think she could have set up a school herself.
All the same, she felt thrilled on her first tour of the renovated library that has become her daughter's first school.
"To walk in to this building - it is amazing," she said.
The government expects hundreds more free schools to open in the next four years.
It will be some time before there is evidence about how they are doing. England's schools inspection service, Ofsted, says all new schools are inspected within two years of opening.
At the same time, children at the new schools will do the same tests and exams as those at other state-funded schools - and all eyes will be on those results.