I applied to this Fund Accountant role through seek.com.au with no relative work experience fresh out of university with a combined Accounting and Economics degree. I had really strong results and was approached very quickly after having applied (2-3 days). The first step in this process was to undertake a telephone based personality interview in which a member of the SS recruitment team asked a number of normal questions to get a guage on the candidates personality. For example... Why do you want to work in the Finance industry? What draws you to State Street? What do you look for in an organisation? etc etc.
If you pass this quick (15 min) phone based interview, you will be asked to interview with a panel of senior stakeholders in the organisation. My own interview was with three such managers and was very laid back and easygoing in terms of atmosphere. This interview is basically a personality test and a bunch of questions that help the interviewers determine your character, morals and I guess competence. Questions I was asked include how I see myself interacting in a team environment, what sort of challenges I have faced, how am I accurate and detail oriented etc etc. They also asked some basic accounting and finance related questions and hypothetical situations so be ready for that as well.
All in all it was a very warm and friendly interview allowing you to ask any questions you may have of the organisation and for SS to find out more about you as an individual. SS ended up calling me the very next day and offering me the job on the spot.