The Black Rat is believed to have come from southern Asia. Documentation shows them as far back as the 1200s. They then got into ships carrying exports of food and textiles. In Europe, they quickly earned a bad reputation for their destructive nature. Rats would often contaminate and destroy the items on ship that were meant for exports.
With the rats' traveling nature, fleas infected by plague would jump on the backs of rats and plague would continue to spread.
During the 1800s in England, wild Norway rats were kept and bred mainly for sport. Rats were the prize for dog hunts and similar activities. Terriers would compete against each other to kill the most rats in a specified time.
At that time, Rat Catcher was a common municipal job.
In the early 1800s, rat baiting became sport: you'd bet how many rats a dog could kill and then put them all together in a pit. Rat Catchers made extra cash supplying rats for the games, an incentive for them to catch them live and keep them in cages. They started breeding them. Then they started liking them. The Albino was the first color oddity they experienced and soon they began breeding for other interesting colorations. By the mid 1800s, rat baiting was outlawed.
Rats soon established themselves as pets. Author and illustrator Beatrix Potter kept a pet white rat and so did other ladies of the time. In the two centuries since, domestic Norways have become more docile than the wild Norways.