The pupil of an eye can come in some strange configurations, from scalloped (Tokay gecko) to square (octopus) to W-shaped (cuttlefish), but the pupils of cats come in two shapes -- round for the some of the great cats and slit for the small cats, including Fluffy on your lap.
Among the great cats, lions, tigers and cougars have round pupils. Round pupils give good vision in the daytime, and they can close to pinpoints to protect the sensitive inner structures of the eyes from too much light. They can also expand in low-light situations, such as dawn and dusk, to allow some night hunting.
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Slit pupils can open and close faster than round ones, and wider, too. Your cat's eyeballs aren't much smaller than yours, but their pupils can open three times larger than yours. This lets her take advantage of the smallest amount of available light -- including starlight and snow glow -- for nighttime hunting. Jaguars and leopards haunt the dimness of the tropical rainforest but also come out occasionally on the open savannah to hunt at dawn and dusk. Because they spend most of their time in semi-darkness, slit pupils work best for them.
You won't find horizontal pupils on any cats, but lots of grazing animals -- goats, sheep, cattle, horses, kangaroos, hippopotamuses -- have them so they can see big cats (or other predators) sneaking up on them. They have three-dimensional vision for 330 degrees: almost all the way around their heads. That means that when you're riding a horse, he can see you sitting on his back.
Cats that hunt primarily at night or in low-light conditions have vertical-slit pupils. Because they are predators and not prey, they don't need to see what's sneaking up behind them -- they're doing the sneaking. Vertical slits work well for domestic cats and many small wild cats. With vertical-slit pupils and horizontally opening eyelids, cats have exquisite and precise control of the amount of light that enters their eyes. They can even express feelings with the pupils of their eyes. If Fluffy's pupils are slits in daylight, she's calm and relaxed. On the other hand, if her pupils are dilated round in bright light, something's wrong -- she's probably ready to run for her life or kill something.