I applied online via Morgan Stanley's website. I received an interview request about 1 week later. The phone interview is either 2 x 30 minutes, or 1 x 45 minute interview (depending on availability). I had the 2 x 30 minute sessions; they were straight forward. First session were high level design questions and technical knowledge, as well as an intro to the IT side of Morgan Stanley. The second session consisted of questions regarding data structures and algorithms - no coding, but expect to explain your reasoning well.
I was invited to an onsite interview in Montreal about a week later (the "superday"), scheduled for 2 weeks out. Trip is fully expensed, with a night hotel stay if you are flying from out of Quebec. The interviews are from 11:30am-5:00pm, so there is leeway to fly in early if you wish.
The onsite had several portions - as others mentioned, a group activity/panel session and lunch lasting 2.5 hours, and 3-4 technical interviews (depending on availability). There were about 22 people for the onsite interview; lunch was served on arrival, and then we dove into a panel session where former interns and current graduates of TAP (technology analyst program) came to share experiences/detail projects, etc. This was actually very helpful - you get a decent amount of time to ask them questions, so make sure you use it well.
Group activity is straight forward - it was a team building/communication activity in a group of 4-5. For us, it was building a free standing structure with uncommon materials. I think here they're mainly looking for how you interact in a team, leadership qualities, and 'soft' skills.
I was scheduled for 4 x 45 minute interviews, but only ended up with 3 as one interviewer had to cancel. They all took place, 1:1, in a common area - multiple tables like an exam hall. The interviews were unorthodox to say at the least; they seemed to tailor them based on your background and what 'stream' they were interested in putting you in (even though at this point, your position/role is unconfirmed/not final - that's decided after the interview). While some others had all their interviews on strictly data structures/algos (typical to that of Facebook/Google/etc.), mine were heavily based on networking, infrastructure, and troubleshooting. I was surprised at the focus on the networking, given that I had limited knowledge in that area (but I did have testing experience).
To sum up the interviews: be prepared for everything - if your resume was tailored to be more of a generalist, expect infrastructure/networking type questions (e.g. explain what happens between the time I enter www.google.com in the web browser and a page showing up). If you have solid software development experience, expect heavy data structures/algorithms, including SQL. I spoke with 2 people from the infrastructure team, and one from the QA PM (quality assurance project management) team; only the latter asked me a broad variety of higher level technical questions. The former 2 drilled me front and back on the breadth of my networking experience (e.g. SSL, TCP handshake, how the internet works, TCP vs UDP, etc.). I was expecting all data structure/algorithms questions, but received none.
Received a rejection 1 week later. Overall, it was well organized, and they communicated well every step of the way (you will receive an email regardless of good or bad news). The interviewers (save maybe 1) were all very friendly and open to talking about their work. Great culture/emphasis on retaining talent and learning. However, I'm disappointed at the rejection, as I feel if I had different interviewer(s) I would have been better evaluated.