Rubbing up against humans
It's well known that cats are olfactory creatures that rely heavily on their sense of smell to learn information about the environment around them. But it's less commonly known that, when cats rub their heads or push up against you, they're marking you with their scent. This action is a show of affiliation and a way for them to maintain connection to the humans around them.
Batting food out of their dishes
Why do cats paw their food out of the bowl to eat it off the floor? The answer lies in the basic instincts of cats. In the wild, a cat would have to scope out their prey and ambush it before getting to the eating part. A domestic cat batting food out of its bowl is just flexing its predatory muscles.
Running around the house at night
There are a few reasons why our feline friends love a mad dash around the house in the wee hours. It could be stored energy (we know how much they love to laze around when the sun's out); there could be another animal outside the house; or they could even be reacting to prey, like mice. Don't get mad at your cat for this behaviour – try and find the source before you jump to any conclusions.
Kneading with their paws
Most cats start that pushy-pushy action, known as kneading, when they're just kittens – a nursing kitten instinctually kneads its mother to stimulate milk production. Later in life, this behaviour often continues as a loving action (you'll notice many cats simultaneously purr and knead at the same time). If your cat has long claws and it hurts when they knead you, don't punish them for this ultimately loving action: a simple solution may be to trim their nails so they can show affection without leaving behind any scratch marks.