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Regular Expression Match Operators

Operator	Description	Example
~	Matches regular expression, case sensitive	'thomas' ~ '.*thomas.*'
~*	Matches regular expression, case insensitive	'thomas' ~* '.*Thomas.*'
!~	Does not match regular expression, case sensitive	'thomas' !~ '.*Thomas.*'
!~*	Does not match regular expression, case insensitive	'thomas' !~* '.*vadim.*'

POSIX regular expressions provide a more powerful means for pattern matching than the LIKE and SIMILAR TO operators. Many Unix tools such as egrep, sed, or awk use a pattern matching language that is similar to the one described here.

A regular expression is a character sequence that is an abbreviated definition of a set of strings (a regular set). A string is said to match a regular expression if it is a member of the regular set described by the regular expression. As with LIKE, pattern characters match string characters exactly unless they are special characters in the regular expression language --- but regular expressions use different special characters than LIKE does. Unlike LIKE patterns, a regular expression is allowed to match anywhere within a string, unless the regular expression is explicitly anchored to the beginning or end of the string.

Some examples:

'abc' ~ 'abc'    true
'abc' ~ '^a'     true
'abc' ~ '(b|d)'  true
'abc' ~ '^(b|c)' false

http://database.sarang.net/database/postgres/manual/manual-7.3/functions-matching.html