The Conan Exiles site has been update with a -beefy- post all about the game's pet system. It begins with a list of what pets players can expect to try to tame, and then provides information about converting them from young creatures to full adults, as well as what pets can be used for by players.
Pets that can be tamed:
To begin rearing an animal, you will need to obtain a baby or an egg. These can be found in the world, and on certain (rare) vendors. To pick up a baby animal in the world, simply press the interaction button when you have it targeted. Eggs will hatch after a certain amount of time and produce live offspring, which will sit in your inventory.
- Jungle Birds
- Big cats (Lions, tigers, jaguars, etc)