Pet adoption usually refers to the process of taking guardianship of and responsibility for a pet that a previous owner has abandoned or released to a shelter or rescue organization. Common sources for adoptable pets are

• Animal shelters, in the case of dogs also known as dog pounds
• Rescue groups
• Pets found loose or stray without identification, and which are unclaimed by any owner
• Advertisements placed by individuals trying to find a new home for their pet
• Pets that have been abused or neglected and have been confiscated from the offending owner
• A fast growing source is online pet adoption. These sites have databases of pets being housed by thousands of animal shelters and rescue groups, and are searchable by the public. The Shelter Pet Project, a unique pet matching service; Let's Adopt, a global animal rescue and pet adoption organization; Pet Search Party, which covers Canada and the United States, and Petfinder.org, covering the United States, Canada and Mexico; are four well-known online pet adoption agencies.

Dogs adopted from shelters are often referred to as shelter dogs or pound puppies; dogs adopted from rescue organizations are often called rescued dogs or rescue dogs Similarly, cats adopted from rescue organizations are commonly known as rescue cats. Many shelters and rescue organizations have put together informational websites to help the public choose the right pet for their family.

Pets are taken to animal shelters for many reasons.

• Breeding: Backyard breeders are a leading cause of overpopulation because they usually produce more dogs than they can sell and often produce animals that do not meet stated breed standards.
• Death: Owner dies and no one in the family wants to (or can) keep the pet.
• Changed circumstances: Financial or living arrangements change drastically and people feel they can no longer provide an appropriate home for the pet. This might also include someone having to move to a new living situation where pets are not allowed.
• Second thoughts: A pet purchased on the spur of the moment or as a gift for another person (frequently for Christmas). Often the owner discovers that caring for the pet is much more work than expected, or requires more space or exercise than they are prepared to give.
• Lost pet: Pet leaves home or cannot find its way back, and carries no identification tags or microchip. The owner does not succeed in finding it (or makes no attempt to do so). See also Lost pet services.
• Health: The owner experiences severe health problems that make it impossible to care for the pet. Or the pet itself is diagnosed with a medical condition the owner is not prepared or willing to address.
• Practice babies: Shelters use this term for animals that have been adopted by couples and which are then abandoned when the couple separates, or when a human baby comes along and the owners no longer have the time or inclination to care for their pet.
• Moving across borders: People leave the country; quarantine laws in some countries can be traumatic to pets and owners, so to avoid the stress, the pet is surrendered to an animal shelter.
• Allergies: Many owners claim to have developed allergies to their pets, or that their children have developed allergies to their pets.

People deal with their unwanted pets in many ways. Some people have the pet euthanized, although many veterinarians do not consider this to be an ethical use of their resources for young and healthy animals, while others argue that euthanasia is a more humane option than leaving a pet in a cage for very long periods of time. Other people simply release the pet into the wild or otherwise abandon it, with the expectation that it will be able to take care of itself or that it will be found and adopted. More often, these pets succumb to hunger, weather, traffic, or common and treatable health problems. Some people euthanize pets because of terminal illnesses or injuries, while others even do it for common health problems that they cannot, or will not, pay for treating. More responsible owners will take the pet to a shelter, or call a rescue organization, where it will be cared for properly until a home can be found. Homes cannot always be found, however, and euthanasia is often used for the excess animals to make room for newer pets, unless the place has a no-kill policy. The Humane Society of the United States estimates that 3-4 million dogs and cats are euthanized each year in the US because of a lack of homes. Animal protection advocates urge people to spay or neuter their pets and to adopt instead of buying animals in order to reduce the number of animals who have to be euthanized.

To help lower the number of animals euthanized, some shelters have developed a no-kill policy. These shelters keep their animals as long as it takes to find them new homes. City shelters rarely have this policy because of the large number of animals they receive. No-kill shelters are usually run by groups that have volunteers or individuals with enough space to foster pets until a permanent home can be found. However, many of these groups and individuals have a finite number of spaces available. This means they will not take in new animals unless a space opens up, although they will often take back pets that they have adopted out previously. Sometimes they try to find the dogs foster homes, in which the dog is placed in a home temporarily until someone adopts the pet.

The central issue in adoption is whether a new owner can provide a safe, secure, permanent home for the pet. Responsible shelters, pounds, and rescue organizations refuse to supply animals to people whom they judge unable to supply the animal with a suitable home. Sometimes, a new owner may face training or behavioral challenges with a pet who has been neglected, abused, or left untrained. In the vast majority of cases, patience, training, and consistency of care will help the pet overcome its past.