In addition to expanding your own spellbook as levels progress, you can buy your pets skill grimoires from warlock pet trainers. These will teach your pets new spells and abilities.
Note that you must have the appropriate pet summoned to learn it new spells through the grimoires.

imp

voiowalker

Succubus

Felhunter

Felguard

You will find further info on pets in the Soloing, Grouping, Raiding PvP, and Enslave Demon chapters.