FYI: Parsing and compiling in the programming language sense are orthogonal problems. Both are major challenges in cpp compilers.
(And just to be completely clear, I'm not saying that the difficulty of parsing C++ makes it miserable to write a compiler. I'm saying that the difficulty of parsing C++ makes it miserable to run a compiler.)
How so? In Ada, Fortran, C, C++, Java, Python, etc. parsing is one of the many phases of compiling. Far from being orthogonal problems, parsing is a sub-problem of compiling.
YACC was called "Yet Another Compiler Compiler" because back in the day parsing was the bulk of compilation, now it's relatively minimal.
When we parse a string, we go up from low-level human-readable strings to intermediate parse trees to a high-level AST.
A process of compilation goes down from some kind of a high-level internal representation through phases to something that is close to the target low-level language.
It can go down from an AST, or LLVM-s internal representation, or whatever.
Problems solved by both processes are different:
1. Parsing is about finding string patterns (using regexps or PEGs or whatever) and representing these using a more strict high-level structure. The structure is usually tree-like but is also often a graph.
2. Compiling takes something high-level (a tree, a graph, etc) and emits something different, usually simplified.
A good example is a typical lisp implementation where the parser is trivial but compilation phases represent numerous simplifying phases.