Many monsters can now be captured and turned into your own personal pets. Pets can be obtained through regular Drops, Events, the Item Mall and Quests.
All Pets in-game come in the form of a Consumable item (found in your Consume Inventory). To activate them, simply Double-Click on their icon in your Inventory and they'll then follow you everywhere you go.
You can only have one pet equipped at any one time. Pets will last indefinitely until their expiration date which is shown on their tooltip when you hover over its icon.
Many pets in-game give added benefits when active, such as stat increases or the ability to automatically pick up your drops. Any benefits they give are shown on their tooltip when you hover over its icon.