Depending on the video (i.e. Cinematic or Gameplay) we'll either use some in-house software (Jessica), or simply fire up the client and record from there.
Jessica allows us to pull in any object or effect that exists in-game and in most cases animate them. It's not really designed for this at all, so it can be quite a lot more tricky to use compared to your normal 3D suite such as Maya (think animation by maths). We still prefer using the Trinity engine for our videos as it maintains the right look and feel for the EVE universe. I think we're very lucky that the EVE client assets are such high fidelity that we can do this!
Of course there's color grading and post effect work done afterwards using software suites (AE etc) to get that cinematic feel where needed.
But yes, it's a lot of fun, I still can't quite believe they call this a job.
There's more info on trailers in this
interview on Massively!