Compilers are like puzzles to be solved. They are so deeply coupled internally and so grounded in pure logic that in many cases, features of the languages implement themselves as the logical consequence of the way the compiler it's constructed.

Learning them also teaches some skills on how to subdivide the solution to a really complex class of problems into comprehensible chunks.

Heck, there are many seemingly unrelated problem domains that can borrow solution strategies from compiler design and implementation.

It definitely is a nice tool to have in your tool belt.