The entire process took a bit long because I am currently working in a different country than the office I applied at. For the internship I went through 1 interview + 1 computer based test on the first round, 2 interviews on the second round and 3 interviews on the third round. Most of the interviews were standard BCG: 15 minutes fit, 30 minutes case, 15 minutes my questions.
During the first stage, a Principal of the firm was in London (I currently live in the UK) to do some business for the firm and gave me the first round interview, together with the problem solving test on the computer. I found the problem solving test as difficult as McKinsey PST: while you do have access to a calculator in this case, you also have 25% less time to go through the same amount of questions, and on top of that questions required you to navigate through multiple exhibits at the same time, not just the last one.
During the second stage, the HR agreed to wait until I was in my own country and had the second round directly in the office. Alternative would have been to have a conference call, but I preferred to be there in person. 2 interviews this time, standard format.
By the time I got to the third stage, I was back in the UK for work. This time the company wanted definitely to have me back in the office to meet the partners, therefore flew me in on the thursday to have the interview on the friday. First and third interview were again standard. During the second interview (with a senior partner & managing director) my interviewer wanted to make sure that given my background (engineering + phd in engineering) I really wanted to work in consulting. So basically he questioned me for 40 minutes on consulting, my motivation to do it, how do I understand the industry, what are the success factors in consulting (as an individual and as a firm), who are the main competitors, what are the challenges and the threats for BCG, what are the differences of consulting in the rest of the world and in the country where I applied. All of this was done in a skeptical and not friendly way, but I suspect he was grilling me to do some kind of stress testing and see if I could keep my cool with a difficult client.
HR was extremely supportive throughout the process, and every interviewer I met was very polite, interested in me and pleasant to have a conversation with. Excellent experience.