Basic knowledge questions based on your profile and area of interest. Interaction with the professor and discussion about the project. Relevant explanation of how the work should be done and what I should bring to the project.

Applied for a phd. Professor was for some weird reason paassed on the recruitment to her grad students who clearly by no means did not belong there and had no business interviewing a candidate who was much more experienced than them (industry experience). I have appeared for many industry interviews and have never had a more intrusive questions asked. They never introduced themselves to begin with, never gave an overview of the lab work or the research projects, did not bother or give me a chance to ask any questions nor did they realise that an interview is a 2 way process where both the interviewer and the interviewee judge each each others compatibility. Some of the interview process and questions were so insulting and horrible that I wanted to quit in between the interview itself - having said that I dont blame the grad students and it was obvious they were in an unfamiliar environment.