Push-ups are a powerful exercise for building a powerful chest.
What makes push-ups superior to the bench press, is that push-ups are more of a whole-body exercise. You have to engage your abs and your legs to hold your body straight while it moves through space.
The only downside to push-ups is you can't adjust the weight as easily as you can with the bench press. But the solution to that is the weighted push-up.
Here's a video that shows how to do the weight push-up:
Personally, I prefer to use a set of weight plates. Get yourself a durable backpack, stuff it with the plates and crank out those pushups.
Put in enough weights so you can only do 3-4 sets of around 8 reps. Rather than increase your reps over time, it's better to gradually increase the weight. This conditions your body to get stronger and grow more muscle, as opposed to focus on increasing endurance.