Pet

Pets are mobs that are controlled, to a certain degree, by certain player jobs, and also beastmen who have these jobs as well. For convention sake, we will call the controlling character the "master". A pet follows his master around, if able, and assists him in battle. Currently, four jobs can use pets; Summoner, Beastmaster, Puppetmaster, and Dragoon. A Bard has the ability to charm a pet, but will not be able to control the pet without Beastmaster as a subjob. Each has pets that are unique in how they function, and how they assist their master.

Summoner Avatars
A Summoner uses magic to call forth a celestial or elemental avatar as their pet, which assists them in physical battle, as well as using other abilities known as Blood Pacts. These avatars will fight when commanded, and will defend their master automatically if they are attacked (unless they are otherwise occupied).

Beastmaster Pets
Certain mobs can be charmed by a Beastmaster and commanded to fight along side them. The following mobs can be charmed:

Beastmasters can also use the job ability Call Beast if they have one of the Beastmaster jugs equipped and can call a beast to aid them.

This link contains other job abilities that affect pets as well as how pets affect Beastmaster's.

Puppetmaster Automaton
Puppetmasters use constructed automatons to assist them in battle, relying on various attachments to augment their pet's abilities. These automatons can be outfitted with different frames to suit the different needs of their master. Some examples are melee frames, ranged attack frames, and magic casting frames.

Dragoon Wyvern
Dragoons share a bond with an infant dragon, which they can Call to assist them in battle, aiding the dragoon with breath attacks and healing abilities. A Dragoon's wyvern is not commanded to fight, it merely follows the example of its master. A wyvern will only fight if the Dragoon is engaged with a mob, and will disengage when its master does so. A wyvern's abilities are dependant on the subjob chosen by the dragoon, see Dragoon Wyvern for more details.

Beastmen
Beastmen that are classified as one of the four aforementioned jobs may also summon their pets to assist them. Beastmaster mobs will summon pets relevant to the area (usually ones that link with others of their kind). Summoner mobs will summon elemental spirits to assist them, or more powerful celestial ones if the beastman is particuarly powerful. Puppetmasters will have automatons aiding them, but these beastmen only appear in TAU areas. Beastmen who are Dragoons will normally not call a wyvern (except in TAU areas), but very powerful ones may, and Notorious ones almost certainly will.

/ignorepet
Recently, a new command was added to allow players to ignore fellow player's pets. When this command is turned on, a player will no longer be able to target (and be hindered by) other friendly player's pets. They will still be able to target Beastmen's pets, as well as pets of players in PvP areas such as Ballista, but when scrolling through targets, normal player's pets will not be targettable.