Cats are everywhere. It's impossible to count the total number of cats globally, but they are estimated to number between 600 million and a billion. With dogs, they are one of the two most common pet or companion animals in the world, and yet pet cats are clearly outnumbered by feral cats and street cats. My book, Cats: A History, explores the histories of these major types of cats – feral cats, street cats, and pet cats – and the relationships that humans have had with them over thousands of years.

This is the first long-term history of cats. It begins with the cautious approach of wildcats to human settlements about 12,000 years ago to feed on rodents attracted to grain supplies. It ends with cats in the modern world, where pet cats are beloved companions and where feral cats and pet cats allowed to roam outside are condemned for their impact on wildlife. In the intervening period, cats have been regarded as useful rodent-killers (and in Ancient Egypt as snake-killers), associated by Christians with religious heresies and witchcraft, appreciated and valued by Muslims, thought of by men as socially disruptive embodiments of women and women's sexuality, and condemned by nationalists as noxious aliens that should be exterminated.

It's this volatile variation in attitudes towards cats that makes their history so interesting. For thousands of years, cats have been fairly consistently valued for their skill in killing rodents that preyed on things valuable to humans. They killed rodents in grain stores, in bakeries, in private dwellings, and on-board ships. They took care of rodents that chewed books and papers in libraries.

But while appreciated for these services, cats began to be associated with heresy, witchcraft, and magic. Witches were accompanied by many animals – goats and horses, for example – but cats are most often thought of as witches' familiars. At the beginning of Macbeth, Shakespeare has a witch call to her cat.

The explanation of these links is probably that cats were associated with women and women's sexuality. From the Middle Ages onwards, cats were described as difficult to control, deceitful, selfish, and promiscuous. These were characteristics that men attributed to women, and comparisons of cats to women were common. By the nineteenth century, cats were likened to prostitutes.

With the rise of nationalism in the nineteenth century, cats became thought of as outsiders. The first cats, which descended from wildcats, originated in the Middle East, and so they were widely thought of as what we now call 'invasive species'. In the 1800s, many people drew attention to the harm cats did to wildlife, especially birds, and there were calls for cats to be exterminated. In Germany in the 1930s, a Nazi declared that cats "came from the east" and did not belong in Germany. He called them "the Jews of the animal world."

At the same time as hatred of cats intensified, so did appreciation of them. In the late 1800s we see cat-shows and evidence of pet cats in some middle-class households. But it was not until after World War II that pet cats became common. In this sense, pet cats on a mass scale occupy only one per cent of the time that cats and humans have had relationships. That's why it's so important for a history of cats to cover not only pet cats, but also the more numerous feral and street cats. They have longer histories.