I had two interviews, fairly close together in the morning, with each one lasting about 40 minutes. Both of my interviews consisted of two interviewers. The interview were focussed almost completely on problem solving. I didn't have any tests to take. Current students took me to both interviews and reassured me on the way which helped calm some nerves

I would say both interviews felt ok at the time. The problems given to me were quite varied; I was asked problems on graph theory, probability, and geometry. I remember misunderstanding what one of the questions meant, but once I had asked for clarification I made progress on the problem, so there's no harm in asking this. Some of the problems were quite open ended, and if I was stuck on what to say they sometimes gave a small hint to put me in the right direction, or to think differently about a problem.

The best preparation for interview, and in fact for applying to maths at Cambridge in general, is to start practicing STEP questions. These teach you to think more about a problem compared with A level questions, and so should prepare you well for working through problems in the interview. I started doing this as early as the summer of year 12 and this helped a great deal with getting in.

It's best not to stress too much about interviews, as it's just one factor of many they take into account when considering applications. It's also worth pointing out it is very hard to judge how well an interview went so it's not worth worrying about afterwards.