The interview questions and structures were pretty standard when compared to other companies that I also interviewed with, such as Apple, Facebook, Google, Walmartlabs, etc.. It included a screener, phone interviews and onsite interview. Interestingly though, Microsoft's screener was an online test of basic math and probability. In terms of the logistic of the process, I got a little confused for having to deal with multiple recruiters within Microsoft. However, they were all friendly, prompt and reasonably helpful.
Questions asked include my education and research background, statistics, basic probability, machine learning and coding. Interviewers came from different background and are experts at what they do, so be prepared for questions that require some well thought out answers.
Microsoft is pretty generous for their onsite interview, so you will have a good time (not the best though, Adobe offered $100 daily meal reimbursement =p ).
Overall, the experience was great. It was quite different than the impression of a middle age corporation that I had in mind before I went to the interview. Employees there are young and enthusiastic in their work, at least for the team I interviewed for. Management also seems to be ambitious in what they want to achieve (in a positive way).