Regular expressions (RegEx) are patterns used to match character combinations in strings. They arose from Stephen Kleene's work formalizing regular languages in the 1950s. RegEx can match words, ranges of characters, word sizes, and perform string matching. Common uses include password validation, login, search operators, spam filtering, data scraping, and text processing. In C++, regex_match is used for matching and regex_replace for find-and-replace operations.