Comparison of various regexp syntax: Regexp Syntax Summary

Learn about Perl regexp: perlrequick, perlretut, perlre

vim: I began learning about regular expressions from using Vim's regexp, and I can attest to its flexibility + features. When you say vi, you're most likely using vim in vi-compatible mode - so don't limit yourself and do enable Vim's full features (with :set nocp). Vim allows you to visually learn about regexp matching with highlighted search:

    :set hlsearch
    :set incsearch
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sed: You can replace sed commands with perl. You're better off in the long run learning Perl, IMHO.

grep: Beyond simple regexp, there's ack - use Perl regular expressions!