When World of Warcraft released their Mist of Pandaria expansion in September of 2013, a new feature they added was 'pet battling'. Very 'Pokemon' like, you are able to catch pets and battle them to level them and defeat hard trainers. There are other ways than just catching them to obtain different pets in the game however. You can also obtain rare pets as drops from monsters, attending Blizzcon, loot cards from the WoW TCG, purchasing Collector's edition of WoW's expansion, some quests even award battle pets and some can even be bought via the WoW auction house.
Is WoW pet battling fun? In my opinion, yes! I just started doing them at the start of this new year and have been addicted ever since. Why is it so fun? Once you get past the initial hump of getting your first team of 3 pets to level 25, it becomes easier to level new pets and rewarding. The more pets you have, the easier it is to down the harder trainer/events. Let's talk about what this all means: When you first start pet battling, all your pets will only be level 1. The pets you have to start are ones you've accumulated in the game prior to the point, just sitting around in your pet journal. Each pet has a 'type', which are as follows: Aquatic, Elemental, Mechanical, Flying, Magic, Undead, Beast, Humanoid, Dragonkin, and Critter. Each type has a special advantage, a weakness, and a resilience. Here is an example: Critters are immune to stun, root and sleep effects(this is a nice advantage), but take 50% extra damage from all Beast type abilities, and take 33% less damage from Elemental attacks. There are many different team compositions to run with for each fight. Note, a certain class of pet might have different type attacks. For instance, a Beast type pet may have all Beast abilities or may have none and only other types like magic or humanoid. This makes everything more interesting.
What are the rewards? Skipping ahead to why it is so rewarding can be broken down into two parts, achievements and gold. As you collect and battle pets, you earn different achievements, which can feel quite accomplishing. Some of the achievements give you extra special rewards, such as titles, a Safari Hat used to give your pets 10% extra experience, better traps to capture more pets a little faster, rare pets only obtainable through the associated achievements, and one achievement actually gives you a sack of 3,000 gold, which is quite substantial in WoW. On the other end, once you unlock the trainers as dailies, you can make a nice bit of gold a day from battling them. Some also give you bags that can contain rare pets in them as well and other fun items. On a harder level, there is a weekly quest to win 10 PVP pet battles (against other pet battlers, just like you) that has great rewards too, such as a pet treat that gives you 50% extra pet experience for one hour.
Overall this is just a summary of certain parts of pet battling in WoW. If you like Pokemon or similar type games, you will probably enjoy the in-game aspect of pet battling in WoW. Pet battling may be a side experience in WoW, but does take skill, time and can reap some great rewards. If you have a WoW subscription and have time to play, I recommend at least giving it a shot. It is also a great way to help level alternative character because if you are not the maximum level in the game on your actual character, you also gain a nice bit of experience for each pet battle, which can be a very fast mode of leveling. So, yes, you can level yourself and your pets at the same time!