Unfortunately what we nowadays call "regular expressions" aren't the regular expressions from math class -- they can match against much more than regular languages. I believe PCRE, i.e., the "regular expression" language for most regex libraries, is Turing-complete though I can't find a citation for that right now.
HTML is not a regular language.
Programming languages are not a regular language.
Generally if there are opening and closing statetements -> it is not a regular language.
Something that isn't a regular language, cannot be handled by regex.