Animals have always played a big role in human history, right back to prehistory. First, they were hunted by humans, but when humans shifted from hunting to farming, humans and animals started to live together. The first wild animal to be domesticated was the wolf, around 12,000 years ago. Many other animals were domesticated, including pigs and sheep, some 9,000 years ago in the Middle East, cats around 4,000 years ago in Egypt, and rabbits in Africa about 1,000 years ago. We can see this in artefacts from the time, such as wall paintings.
In the Middle Ages, a pet dog became a real status symbol. Only very wealthy people could afford one. The church was against pets, because it felt it would be better to give the food to the poor. It was not until the late 18th century that it became acceptable to keep pets in Europe.
We still use domesticated animals today, for food, as transport and for their milk, skins, eggs and meat. Some animals have a very specialised role, like guide dogs for the blind. Or decorative fish.
Only a few species of animals, with the right characteristics, have been domesticated.