are a great exercise you can do anywhere.
If you don't get bored with doing push-ups all the time, they could be your only chest exercise!
The only drawback with push-ups is they can be hard on the wrists for some people.
If they are hard on your wrists, pick up push-up stands such as the perfect push-up, which will run you from $10-30.
you elevate your feet and keep your hips up, and spine in neutral alignment, you will primarily work your upper chest, and shoulders.
Remember you are never lowering your face towards the floor for push-ups.
If your hips cannot stay up in neutral alignment you may need to work on some core exercises. You can read all about core exercises here:
Trainer Mike Behnken, MS, CSCS