In England and Northern Ireland, and for non-Welsh students in Wales, full-time undergraduates are liable to pay tuition fees of up to £3,225 a year (2009-10 rates).
The poorest students are eligible for non-repayable support at up to the same amount.
It works like this:
In getting the tuition fees legislation through Parliament in 2004 ministers accepted two amendments.
The first imposed a duty on the education secretary - rather than just a power - to impose the £3,000 cap on any university that tried to charge higher fees.
The second ensured that any move to raise the £3,000 limit after 2010 would require a vote of both Houses of Parliament.
Why did the government want to charge students more?
Universities said - and still say - they need more money.
The government says graduates benefit from having gained a degree - through wider career opportunities and earnings - so ought to contribute something.
A counter-argument is that the biggest beneficiary from having a more highly educated workforce is the national economy as a whole, so the nation ought to be prepared to invest in it.
Why the term 'top-up' fees?
Because they "top up" what universities receive from the previous capped fee to more like the actual cost of providing the course - which the government says is about four times as much on average.
Ministers used to argue they were not, technically, "top-up" fees - which they previously promised they would not allow - precisely because they would not meet the full cost of tuition. But by 2005 even the Education Secretary, Ruth Kelly, was referring to them as "top-up fees".
The actual cost varies from course to course and institution to institution. In broad terms, courses in science and engineering are more expensive to run than, say, English or psychology, because of equipment costs.
Do the higher fees apply to all England's universities?
Not necessarily. They are properly "differential fees" - they can vary. The government's original White Paper said: "We will give universities the freedom to set their own tuition fee, between £0 and £3,000."
So in theory you might pay nothing - though nobody rushed to advertise such a course.
The bigger dilemma for university vice-chancellors was what level of fee to charge for different courses - or whether to charge the same for all.
In the event that is what happened with £3,000 being introduced everywhere except at Leeds Metropolitan, which uniquely offered fees of only £2,000 a year until 2009 when it raised them in to line with all the others.
To be allowed to charge the higher fees a university has to satisfy the new "access regulator" - Offa - that it has approved bursary schemes and policies in place to increase the take-up of university places by people from the most disadvantaged groups in society - "widening participation", in the jargon.
Offa monitors the arrangements annually.
Aren't poorer students put off by the cost?
Research evidence suggests that is the case. The people most likely to be deterred by the prospect of graduating with substantial debts - and not having full-time earnings while they are at university - are those the government most wants to attract into higher education.
So not only did it abolish up-front fees but limited maintenance grants of up to £1,000 were restored from 2004 and rose to £2,700 in 2006.
If a student's household income is about £17,500 or less, the student is likely to be eligible for the full grant. Partial grants are available for those with a household income of between £17,501 and £37,425.
Universities are "required" to find another £300 at least in bursaries for the poorest students, if they wish to charge the maximum in fees.
Can I get a student loan?
Official student loans continued. Everyone qualifies for 75% of the maximum, regardless of income, and the rest is means-tested.
The maximum amounts for 2007-08 are £4,625 for students living away from home (£6,475 in London) and £3,580 for those living at home.
From 2005 people started repaying everything once their postgraduate income passed £15,000. Someone earning £20,000 a year, for example, would repay £8.65 a week.
Any debts still outstanding after 25 years - from loans or fees - will be written off. Ministers expect most people will have cleared their debts after 13 years.
Did higher fees hit applications to university?
No. There was a dip as they started in 2006-07 but have risen strongly since.
Even the National Union of Students dropped its opposition to fees, campaigning instead against any rise from the index-linked £3,000 level.
What about the rest of the UK?
The issue is different in England, Wales, Scotland and Northern Ireland.
The government's changes applied directly to England and made provision for similar changes in Wales with responsibility for those handed to the Assembly in Cardiff.
To begin with the Labour Assembly scrapped up-front fees and pledged not to introduce variable fees at universities in Wales. In June 2005 it struck a deal with Plaid Cymru, Conservatives and Liberal Democrats.
So Welsh universities could charge the £3,000 (index-linked: £3,225 for 2009-10) but students living in Wales could get a non-means tested subsidy of up to £1,940 a year, which does not have to be repaid.
Students from other parts of the UK will pay the full £3,225. Welsh students who go to colleges outside Wales will also usually pay full local fees - although they will be subsidised for some courses, such as veterinary science, which are not available in Wales.
But this proved unaffordable. The Welsh Assembly Government has consulted on replacing the universal subsidy with a means-tested grant.
The Northern Ireland Assembly also approved scrapping up-front fees, but said this would be too expensive and would contravene equality measures because offering free tuition to all would benefit the wealthy more than the disadvantaged.
The Department of Education and Learning said it saw no alternative but to match the proposed system for England.
The Scottish Parliament has always had devolved power over student finance and decided to scrap up-front tuition fees for Scottish students at Scottish universities in 2000-01.
In fact, students throughout the UK are liable for the fees - the way Scotland's government gets around this is to pay them for those living in Scotland.
After they graduated, Scottish students used to have to pay a graduate endowment which went into a student hardship fund. In February 2008 MSPs voted to abolish this charge, which by then had reached £2,289.
The vote meant current students and those who had graduated in 2007 would not have to pay the fee.
Those who are not from Scotland pay £1,775 a year (at 2009 rates) or £2,760 for medical courses.
What about part-time students?
The government's white paper said "no student will have to pay their contribution up-front or while they are studying". But this was not true for those on part-time courses.
And people undertaking postgraduate study - probably already with debts from their first degree - still have to find the course fees in advance.
Part-timers make up more than 40% of all students in higher education, almost all of them being aged over 21. The average part-time student is aged 37, female and in full-time paid employment - employers pay the tuition fees for about 36% of them.
Institutions can, at their discretion, waive part-timers' tuition fees. There are no regulations on how much they charge for most part-time courses.
The student support arrangements changed from 2004 to give a means-tested, non-repayable "fee grant", while loans were replaced by a "course grant" to cover things such as books, materials and travel.
The maximum available varies with the "size" of the course in terms of its equivalence to a full-time course.
This pattern is now similar throughout the UK but the amounts vary. They are least generous in Scotland.
What about students from abroad?
People from other EU countries taking an undergraduate course in the UK have to contribute the same amount as UK residents locally.
So they get free tuition for first degrees in Scotland, and will pay only the same as Welsh students if they go to study in Wales.
The government is taking steps to ensure fee loans will be recovered from students from other European Union countries who come to study in the UK.
People from outside the EU are charged whatever international rate each university chooses to apply - typically many thousands of pounds.