It has been possible since Oracle database release 10, Regular Expression support with its own set of functions. But getting started with Regular Expressions is not easy. Most database developers would avoid them if at all possible.
With current release of the Oracle database, Regular Expression syntax becomes more important. You can use them to redact data with DBMS_REDACT and to search for patterns using the Match_Recognize clause.
This session covers the basic syntax and gives you an easy introduction with Regular Expressions with plenty of code samples.