Push ups are an excellent exercise to develop a limited amount of upper body muscle, and as far as endurance goes, the sky is the limit. Push ups build muscle, there is no doubt about it — but the amount of muscle will be severely limited unless you begin adding resistance in the form of weight. Adding weight is the only way to build muscle. More push ups won’t do it, that will only build endurance.
When the average inactive, unfit person begins doing push ups, they will see that because their muscles have been severely underused, they will develop rather quickly. After all, the upper body of most people is a not unsubstantial amount of weight in itself — and that weight is being lifted each time a push up is performed.
What happens then, is the muscles will over the course of weeks or months, grow in size in proportion to what the body deems necessary to lift such an amount of weight. Then it will stop. It may well be that you are very happy with the amount of muscle size you have gained, in which case, simply continue as you are.
If you want more, however, you must begin to add weight, just as a bodybuilder would. At this point, you may wish to consider switching to traditional weight training exercises to further your muscular development, such as the bench press in place of push ups.
If not, then the simplest solution is to begin wearing a backpack when performing push ups. Gradually start adding in heavier objects. You’ll find that the heavier the backpack becomes, the more muscle size and strength you gain.
Also, don’t think that just because you are using your bodyweight to build muscle and not weights that you don’t have to eat like a bodybuilder. Your muscles will only grow as big as your diet allows. You need to eat enough to see muscle growth, but not enough to see fat gains. So get plenty of calories from protein and complex carbs!