[alexhutcheson]

All the digital logic building blocks of a processor, from comparators to ALUs up to branch predictors and pipelines, can be defined and wired together in an HDL. If you have a sufficiently large FPGA, then you can "run" that HDL specification on the FPGA to get a working processor.

It's pretty common for computer engineering students to implement a simple RISC processor (often a simplified MIPS) on an FPGA as a class project. In my experience it was a fantastic way to learn the basics of computer architecture.