When you're going through a divorce, one of the things you could be worried about is what will happen to your pets. If you brought the pets into your relationship, it's usually clear that they'll stay with you, but other factors could play a role.
If you have children, for example, you might want to keep your pets with them due to their attachment. If you don't but you spouse wants to keep the pet, then it could come down to who the pet is more familiar with or how you want to handle custody of your pet.
By law, pets are treated as assets, not as people. That means that you don't technically have "custody" of a pet, you either gain the right to own the pet or not. What you can do, if you and your spouse can agree, is work out a pet visitation schedule. For instance, if you're only a few blocks away from your ex's house, you could pick up your pooch on the weekends or share your cat each week.
Something to keep in mind is that even though your pet is an animal, it will take time for it to adjust. In some situations, it's better for only one person to have the pet and for the other to let go. If the pet was purchased for your wife, for example, it's a gift and should probably stay with her. If the pet was a gift for you, keep it. In either case, if you can't agree, you can negotiate or go through mediation to work out a solution.
Source: Huffington Post, "Who Gets The Pets In A Divorce? What You Need To Consider When Fighting Over Fido," Maria Moya, accessed Dec. 06, 2017