Pet Fusing is an action which takes place in the Pet Yard wherein two pets of the same family and rarity are combined to create one new pet of the same family of the next rarity level. Pets which are not the same rarity or not from the same family cannot be fused. Also, the pet yard must be of a sufficient level to allow the fuse (see pet yard. The resultant pet will receive characteristics from the pets used in the fuse. These characteristics are directly determined (the only random outcome is the species, or appearance, of the pet), so make sure to fuse the pets which will result in the outcome you desire!
The Upgrade Pet modal found in the pet yard is used to Fuse two pets together. Clicking Fuse Pet opens the Fuse Pets modal.