transformer vs. component

This should probably be an FAQ sort of thing.  From a design perspective when do you use a transformer, and when do you use a component?

My impression is that a transformer is primarily to convert data from one type to another type and a component is used when you need to change the data, do computations, or take some other action (besides the actions specified in the outbound router).

There seems to be a gray area there that I'd love to hear other Mule users elaborate on...