Hey fellow R4 applicants! Not sure where everyone else is in terms of interviews, but I just finished both of mine over the weekend and today.
If anyone is interested, wrote up my experiences below. FYI, I am a US applicant and both interviews were conducted in the US by local alumni.
Interview 1: The first interview was very casual (as was the second one). We had lunch at a local cafe. It was sweltering hot - I wore a suit but the interviewer was wearing a button up and shorts. Overall, I felt like the interview was much more of a conversation rather than an interviewer. We did talk about things like my background and why INSEAD, but mostly felt like a conversation with someone I met at a coffee shop.
Interview 2: This interview had some of the typical questions that come up like tell me about working on a team, tell me about an accomplishment, what are your weaknesses, tell me about a time when you had culture shock. Basically if you go through the list of questions in this forum you will be set. Other than that, we talked a lot about her experiences at INSEAD and what she felt the strengths and weaknesses of the program were.
Overall, I'd say just write up some questions from the forum on a 3x5 card and drill them and you should be good to go!