Pushups work multiple muscles danny. The are a compound movement, the same as bench press, but you only use your body weight. When doing a pushup, you use your chest, shoulders, tris, and lats (a little) as part of the main movement. Then you also have all the supporting muscle groups used to keep your body in good form such as abs, lower back, hip flexors, quads...etc.
Notice that if you do a good ab workout before you try pushups, you will feel your abs burning too since they are used to keep your body straight and in proper form for pushups.
But, to answer your main question, the 3 main muscle groups used in pushups are chest, shoulders and tris. Generally when your chest is getting fatigued, you will pull your elbows closer to your body and use more of your tris for the last few reps.