What are Oxbridge interviews really like? And how can I prepare for them?

I would firstly stress to my student that getting something wrong in an Oxbridge interview is absolutely fine, and is actually expected and, to an extent, encouraged! Above all, the tutors at these universities are looking for someone who has the passion and potential to grow and develop over three or four years of tutoring, so if they can see you know everything already then this development wont be possible. That said, there are definitely ways to prepare for interview. The interviewers are, as I said, less interested in what the interviewee knows, and more interested in how they think. So, my first piece of advice; get used to thinking out loud. This way, the interview can become a two-way conversation. If you're doing all your thinking internally, you might end up at a good answer, but all your working has been for nothing as the interviewer can't see it! So practice that. Also, the interviewers want to see you demonstrate your passion for the subject. Again, they're not looking for what you know here, but they want to see that you've done some wider reading or viewing, and if you happen to have a snippet of information that you've read that you think is relevant to the discussion, then throw it in! This area is particularly important when it comes to your personal statement; you may not be asked questions on it, but if you are then it's so helpful to know it inside out - after all, your personal statement is the one area you really have control of to show your passion! Final piece of advice; don't try to anticipate or second-guess what might be in your interview and DEFINITELY don't get fooled by tales of horror interviews from the past - they simply aren't true, and if you try to second guess what you'll be given by the tutors, then you'll panic when it inevitably doesn't come up - it's much better to know your personal statement inside and out, and just be adaptable to whatever you get given.