They have, in fact, been around for quite a long time - I first came across them in 2006/07 or so when I was working as an employed employment law barrister at Plumstead Community Law Centre.
Characteristically, the employee with a zero-hours contract doesn't realise the implications at the start of his employment because he gets a lot of hours.
It's only when the work dries up that he finds there's nothing he can do about it because he has no contractual right to any paid hours at all.
The employer will very often refuse to terminate, leaving the employee with weeks of worklessness but but little remedy.
He can't walk out and claim that there's been a fundamental breach of contract because he was never guaranteed any hours and pay in the first place. He usually has to resign with little remedy.
If the employer does terminate his employment, if the employee has over two years continuous service, he can claim compensation for unfair dismissal.
However, the compensatory award he will get from the tribunal is likely to be extremely low as it's linked to his wages at the time of termination - next to nothing.
A sympathetic tribunal might make a substantial award for "loss of statutory rights" - usually only £250-300 - but it would have the discretion to vary that if persuasive arguments were presented by counsel familiar with the long history of this kind of compensation.
I gather from Channel 4 News that some brave soul is trying to tackle zero-hours contracts at employment tribunal via the Part Time Workers Regulations. This might be effective.