Marco Russo points to this very interesting paper on "Analysis Services 2005 Processing Architecture" by TK Anand, which I hadn’t seen before; he also has a good discussion of how this all relates to slowly changing dimensions. Particularly fascinating for me was the section on push-mode processing – I can think of a whole bunch of interesting applications for this functionality when it comes to creating cubes from non-standard data sources and you don’t want to use SQLIS.
If I could make a criticism of such a good white paper it’s that it makes no mention of local cubes. As I noted a while ago here, in AS2005 you can create local cubes using this functionality – indeed, if you run a CREATE GLOBAL CUBE statement to create a local cube and run a Profiler trace, you can see it translated into the equivalent XMLA batch command which defines and then populates the local cube. I’m covering this topic in MDX Solutions 2nd Edition but I can tell there’s a bit more research to do to see exactly how much of what’s in the paper is relevant to local cubes.