Pushups work my chest—and they really make me work. Hard. No matter how often I do them, they never seem to get easier. So while I love what they do for my chest muscles, I hate them because they are so stinkin' hard! And in all honesty, that is the beauty of the pushup. They will always and forever challenge my chest.
And my shoulders, even my arms. In fact, pushups challenge my entire body much like a plank does. And they'll challenge yours, too. Let me break it down: Your chest muscles contract, with a little assistance from your shoulders and triceps, to raise and lower your body. Your abs and back muscles contract to stabilize your shoulders and hips, which work to keep your body in line throughout the exercise—hooray for proper form! And I bet if you focus on them, you'll notice your glutes (i.e. "butt muscles") are a bit contracted, too. So while a bulk of the work is still being done by your chest muscles, these other muscles are working, too. Thus the comparison to a plank.
"What if I do them on my knees?"
My answer to that: no worries! You are still engaging a variety of upper body muscles. Keep your core tight, hands below your shoulders and breathe through the pushup. You'll feel the burn. And if you don't, it might be time for you to get those knees off the floor!