It isnt very complex but it is extremely fun being able to really understand how a CPU works.
I've always thought of the "basic" idea of a CPU as a very fast player piano. What is really interesting, is when you start reading about how player pianos worked. Some of the "later" models actually had some very advanced features, including some basic "logic"/"branching" codes and such.
Then again, Babbage's Analytical Engine was the epitome of mechanical calculation (had it been realized).
Once you get your mind wrapped around what is really happening (how program counters/registers, address registers, data registers, etc - and the logic switching works) - you realize how simple a CPU really is (at a certain level - then you start to learn about things like micro-code, pipelining, etc - and it goes complex again).
A fast player piano, a fast player piano...
;D