I applied through our company's internal site, and got a response within a few days with a time and a place for the initial interview, which took place online (since we were in different cities).
I was asked about my current job, school, courses and prior experiences relevant for the job. I also got to ask question about the position.
A week or two later, I was called in to a second interview. Prior to this, I was asked to complete a personality-test as well as a a couple problem-solving ones.
In this interview, a HR-lady and two of the people I would end up working with was present. Half the time was used to go over the tests while the remaining time was a series of questions/scenarios. What/how would you do that type thing.