Regular expressions and 'capturing parentheses' with 'backreferences'
These extended notions of regular expressions capture more than just the regular languages.  For example, ([ab]*)\1 matches the language $\{ww\mid w\in\{a,b\}^*\}$, which isn't regular and isn't even context-free (Example&nbsp;2.38 of Sipser, Introduction to the Theory of Computation, 3rd edition).

"Regular" expressions that don't match regular langauges can't be translated to finite automata, since finite automata match only the regular languages. A side-effect of this is that many libraries don't even try to compile to automata, which can lead to extremely slow matching, even when a "regular" expression is a true regular expression. Russ Cox wrote an excellent article about this, which goes into a lot of the history, too.