In the past (ninteen-eightees), it was best to use a standard processors as a separate chip.
Today, it is no problem to put down one or more 'standard' processors on a SoC.
It's also quite easy to design your own, so MIPS, Tensilica, ARM and co have to compete against in-house design teams.
We'll use the the Open Risc 1000 in section 3 of the course...