JavaScript

There's a lot of great resources others have given, but as an overview, regex is kind of a mini language for Natural Language Processing. If you work in any kind of field where you have to work with unstructured data that contains things like phone numbers, names, IPs, hostnames, DNS records, etc, it's a very powerful skill to have. Regex is for the most part largely the same across different languages, so if you learn regex for Python or JS or Perl it's largely the same.

The power comes from using regex meta characters. You'll have to look them up a lot to remember what they each do... You will probably have to reference a meta character guide pretty often at first, so it might be a good idea to print out a cheat sheet.

Learning regex was the start, for me, of being able to write applications that could easily be reused.