Popular belief says that dogs are color-blind, and can only see in two dimensions.
Dogs DO see in color… just not the same way that people do. There are fewer cones (color vision cells) in a dog’s eye than in a human’s eye. However, dogs have many more rods (light and motion detectors) than humans do. So they may not perceive colors as well as humans do, but they can see far better in the dark than we do! Dogs can also spot much smaller motions than humans — probably a leftover from the days of hunting their own meals, instead of hunting a dish full of kibbles.
Dogs can also see flickering light better than people can. This means that a dog may see individual frames in a television show, while we see a continuous scene.
But as far as colors go… some veterinary folks believe that dogs lack the ability to see the colors in the spectrum between green and red. Humans, on the other hand, typically can see the whole spectrum. If that theory is correct, dogs see mainly shades of yellow and blue. Another theory is that dogs lack a certain yellow pigment in the lens of their eye that would let them block short wavelengths like blues and violets. Because they can’t block the blues and purples, dogs may be able to see very small hue differences in those colors. Humans have a reduced sensitivity to blue and violet light waves, and cannot perceive these differences as well.
If you want to test your dog’s ability to tell colors apart, you can try this: teach your dog that a particular color of toy or ball or towel always gets a positive response. Give him treats and praise every time he brings you the blue towel. Now offer him a stack of towels, all identical except for the color. See if he brings you the blue one when you ask for it. It’s not totally scientific, but it may give you an idea of your dog’s ability to see color.