Cats have a curious allure. Even the most pampered house cats seem to flaunt their independence, as if to say that they do not really need us to get by. Despite this hauteur—or perhaps because of it—many of us cannot resist bringing these regal creatures into our homes, litter boxes and all. In fact, cats outnumber canines as human companions, although we know surprisingly little about their cognition.

Our partnership with cats is long-standing. Feline DNA suggests that the domestic cat may have split from its wild counterpart in the Middle East nearly 10,000 years ago. In 2014 a study by Michael J. Montague of Washington University in St. Louis and his colleagues identified a set of genes that may have been crucial in the transformation of the prehistoric cat into the cuddly pets we know today. These genes have been linked to key behavioral traits, such as the ability to learn and reduced fearfulness, which would have helped cats adapt to life in human company.

Yet many mysteries remain in deciphering feline behavior and intelligence, particularly in contrast to our growing knowledge of dogs. This gap arose in part because of the more urgent need to study dogs. Negative interactions between humans and hostile or misbehaving dogs are common societal problems.

A bigger reason for our poor grasp of the feline mind stems from the challenges of cat behavior. Whereas the ancestors of dogs roamed in packs and learned sophisticated strategies for interacting socially with other animals, the wildcat progenitors of today's house cats were more solitary animals. The patterns that govern their exchanges with one another and humans are therefore harder to parse. Ádám Miklósi and his colleagues have found that like dogs, cats are able to follow a pointed finger to food, but if the setup is rigged (say, if the bowl is just out of reach), the cat will give up; a dog will creatively strategize or look to humans for help. “If there's a problem,” says anthrozoologist John Bradshaw of the University of Bristol in England, a specialist in human-animal interaction, “cats try to solve it on their own. And if they fail, they just walk away.”

Cats are also tough to manage in the laboratory. “The second you take a cat out of its own home, it becomes nervous,” says Marieke Gartner, a psychologist at the University of Edinburgh. If the cat is in its own territory, Gartner continues, it will react more naturally. As a result, most studies of cats are based on observations in the home rather than controlled experiments in the lab.

Given these challenges, we still have much to learn about cats. We can easily decipher a score of signals from dogs, but, Bradshaw says, “with cats, it's more like five or six.” Some of the signs we know are listed below.

PURR The purr seems to serve multiple purposes: to share emotional states such as happiness or distress; to express urgency, typically when a cat wants to be fed; or to signal stress or injury.

MEOW Cats generally do not meow at one another, but they learn a repertoire of meows to communicate with humans. Typical meow meanings are specific to a given relationship: an owner knows what his or her cat's meow means but cannot necessarily understand that of another feline.

EARS Ears back signals aggression. Ears forward signals interest.

TAIL Tail straight up shows that the cat is fond of you but also acknowledges that you are slightly superior to it.

Tail straight up and puffed out means the cat is angry.

Tail tucked between legs means the cat is insecure, trying to get away or withdrawing from the world.

RUBBING ITS HEAD AND FACE ON THINGS A cat has glands on the corners of its lips, between its eye and ear, and under its chin; this behavior marks territory, and some scientists believe it could signal affection.

LYING ON ITS BACK, BELLY EXPOSED The cat is relaxed and trusts you.

KNEADING Kittens make this motion to stimulate their mother's milk. In adulthood, researchers suspect the behavior is affectionate and signals that the kneaded individual is in a superior, mothering role.

LICKING Cats of the same size and status groom one another frequently, which is thought to improve bonds and eliminate aggression within the colony. “It's a genuine demonstration of affection,” Bradshaw says, “which in cat societies is very important.”