I applied through Bloomberg careers site. To submit my application I needed the CV and answering some written questions in a form online. After a couple of weeks I received an email invinting me to take a video interview.
The video interview works like this: when you open the link and start, the question to answer shows up on the screen and you have ten/thirty seconds (I don't recall) to prepare it, when the time is up you have around 30 seconds to answer it. There were about 7 questions, 30 minutes in total (ascending in difficulty, I would say, but none really really difficult). The communications until this point were held by Yello, which is the company Bloomberg uses for the video interview.
If you pass the video interview, an HR employee from Bloomberg contacts you and asks about time availability for the following two weeks, in order to held a 30-45 minutes interview with the managers of the departments you are applying to (in my case, Sales&Analytics and Global Data).
A week later I was given a time slot and we held the interview (average difficulty) via a Skype-like website - really nice and professional interviewers.
Two weeks later, the HR employee contacted me to tell me Bloomberg was not going to pursue my candidacy and offered feedback. I asked for it, but was never given.
Some questions: Why Bloomberg? What is excellent customer service? Tell me about a time when you provided excellent customer service? [They describe a situation]... what would you do to ensure excellent customer service in this situation? Do you follow the news? Tell me about some important news you are following?...