Normal human eyes contain three kinds of color-detecting cells called cones, and by comparing the way these cones are each stimulated by incoming light, our brains distinguish red wavelengths from green and blue wavelengths from yellow. Dogs' eyes, like those of most other mammals, contain just two kinds of cones. These enable their brains to distinguish blue from yellow, but not red from green.
According to Jay Neitz, a color vision scientist at the University of Washington who conducted many of the modern experiments on color perception in dogs, our pets' eyes are structured in a similar way to those of red-green color-blind people, whose eyes also lack the third kind of cone normally present in humans.
We can get an idea of what dogs see, Neitz said, if we assume their brains interpret signals from their cone cells much like the brains of color-blind people.
To see blue and yellow, dogs and humans alike rely on neurons inside the eye's retina. These neurons are excited in response to yellow light detected in the cone cells (which are also inside the retina), but the neurons' activity gets suppressed when blue light hits the cones. A dog's brain interprets the excitation or suppression of these neurons as the sensation of yellow or blue, respectively. However, in dogs and color-blind individuals, red light and green light both have a neutral effect on the neurons. With no signal to interpret these colors, the dogs' brains don't perceive any color. Where you see red or green, they see shades of gray. [Red-Green & Blue-Yellow: The Stunning Colors You Can't See]
"A human would be missing the sensations of red and green," Neitz told Life's Little Mysteries. "But whether or not the dog's sensations are missing red and green, or if their brains assign colors differently, is unclear."
Furthermore, like color-blind people, dogs may use other cues to distinguish the color we call "red" from the color we call "green." [Vision Quiz: What Can Animals See?]
"A lot of the time there are good cues to help them figure it out; for example, red objects tend to be darker than green objects," Neitz said. "So, if it's a dark apple, a red-green color-blind person would know that it's probably a red one, and if it's a lighter apple, it may be a Granny Smith."