Blackrock: I applied aaages ago and can't exactly remember what I applied for but I think it's research. Silly me didn't save my answers so I've no idea what I wrote but I'm relying on my surpememe ability to BS to save me in the interview. HR told me it'll be two interviews as well as a numerical though I did an online one quite some time ago.
I think the only reason why they called me for an interview is cos I rang HR twice and left two pretty damn annoying messages asking them, ever so politely, "WHAT THE F**** IS GOING?!!" to which they responded (eventually) by offering me an interview.
Fidelity: it was my an HR chick and it was pretty basic, competency based. Most of her questions was just drilling into my previous answers. I hadn't prepared "why fidelity/research?" answers. I told her that fidelity recruiters came down to my uni for a recruiting event and she wasn't impressed that i'd forgetten their names (was in feedback).
In a nutshell, it's nothing too taxing. Just be able to project your thoughts and answers clearly and be prepared to elaborate on whatever you say. If I remember correctly she told me they're only taking 3 interns into research so I imagine it's pretty competitive. Good luck buddy.