Having approached them at a university careers fair, I applied the day after and received a phone call within 3 days inviting me for a video interview. The questions are listed in many of the reviews here, and not difficult, though one should prepare thoroughly as it is certainly a unique experience.
Having past that, I received another phone call asking me to come to the London office for an interview with the head of HR, with basic fit questions and to test my understanding of the business model.
Three or four days after this, I was asked to perform a case study interview, doing a presentation in front of an analyst, an associate and a vice president. More technical this time, to test the innate understanding of how their business works. Do your research !
Finally, after this I was invited for a final interview with both managing directors. This was a long, nearly 2 hour interview that was very intense and in depth, both in terms of my background and fit and also how well I understood how the business works. It is worth repeating you will be found out in this interview without a very detailed working knowledge of how Alphasights works.
Received an offer over the phone from the managing director himself, and accepted instantly.