Pet doors have been around commercially for the past 30 years. Sir Isaac Newton has actually been credited by some for inventing the cat flap though this is in dispute.

Why would anybody want a pet door? Pet doors are beneficial to both pet and owners for a variety
of reasons. The pet door allows unfettered access in and out of the house or to certain areas of the house. As such, the pet can “go” when it needs to without unhealthy storing of its waste. This would applies to both indoor and outdoor doors, since indoor doors may lead to an area where a litterbox is.

The pet also has greater space to explore, discover, play and exercise, making for a happier freer animal.
He will have more places to hide and shelter, in case of danger or hazards such as weather. More space will also mean a wider demarcation of protection against other animals, both domestic and wild as the pet marks and defends their territory. This will also double as advantageous to the household as the pet can protect it from trespassers, intruders, salesmen, and if you want some fun, the postman.

Pet doors are also advantageous to the pet owner in terms of convenience and time. You don’t have to get up a dozen times to let the pet out, and another dozen, to let it back in at all hours of the night and day. You would not have to stop whatever you are doing to do this neither would you have to cut short and curtail your activities away from home cause the pet is locked indoors.
Pet doors also save owners damage and expense as you would not return home to a scratched up front door. It is also less likely that you would enter the house to find a chewed up sofa, mattress or clothes and knocked over lamps and tables. This is because your pet would no longer be bored or angsty and claustrophobic due to being in a confined atmosphere. Not to forget once your pets got to go its got to go resulting in a mess on your favorite Persian. This also includes vomiting and the need your pet might have to chew up a little grass- with the pet door there is easy garden access.

Pet door features also enable the pet owner to have security and control over pet door accessibility. Some pet door types will have differing levels of security control features. For example a 4 way locking door can either be opened, locked or entry only, or exit only. This would allow the owner to let the pet back indoors and not out again, or let it out and keep it out until a desired time. In addition some pet doors have keys. Keys are either electromagnetic, electronic or infra red devices that are attached to the collar of the pet. These keys signal the door to unlock and allow the pet access. Keys can therefore be used to control which pet in your menangerie you want in and out. It can also be used to keep out the neighbors pet, strays, or unwanted creatures such as raccoons.

Pet door types, sizes, features and pet door training are further issues that need to be considered oncethe purchase decision is made.
All these are covered in the source site.