What is the computational complexity of "real-life" regular expressions?
The following extended regular expression matches the language $\{ ww : w \in \Sigma^* \}$:
$$
\texttt{^\\(.*\\)\\1\\\$}
$$
This language is neither regular nor context-free.
Matching using extended regular expressions is NP-complete; see for example this paper, which discusses efficient algorithms in some special cases.