The Menagerie is located in your garrison, and is relatively central to your pet battling experience for the Warlords of Draenor expansion. I’ve written an overview of the Menagerie feature, as well as several posts outlining the strategies therein.
To unlock your Menagerie, you must beat 3 different single-pet fights during the quest Pets vs Pests. This quest opens up once you have a level 3 Garrison. I’ve outlined the strategies to beat these Pests in 3 different posts:
After your Menagerie is unlocked, you will then be given a daily quest (Scrappin for Horde or Battle Pet Roundup for Alliance) to defeat the current challenge in your Menagerie’s pen, off to the lefthand side of the quest NPC. There are 15 fights in total. Here’s the list in order, and the links to the strategy guides I’ve written for them as well:
Manos, Hanos & Fatos
Squirt’s Deebs, Tyri & Puzzle
Rukus & Brutus
Mr. Terrible, Carroteye & Sloppus
King Floret & Queen Floret
Gromli & Kromli
Grubbles, Scrags & Stings
Jahan, Archimedes & Samm
Fiero & Tirs
Rockbiter, Stonechewer & Acidtooth
Quintessence of Light
Blingtron 4999b, Protectron 022481 & Protectron 011803
To see which pet battle is being featured at the Menagerie today, click here for the pet calendar.
After you win 150 (down from 500 as of a hotfix on 12/3/2014) battles in Draenor & get the Draenor Pet Battler achievement, you can upgrade your Menagerie to level 3, which unlocks a different daily challenge. This challenge also requires you to defeat the opponent in your Menagerie’s ring, but will award an additional bag, the Big Bag Of Pet Suppies, which can contain a variety of new battle pets representative of some of the Menagerie fights.