The Push-up is one of the greatest exercises for developing serious upper body strength.  It effectively trains all of the muscles involved in horizontal pressing (pecs, triceps, deltoids,  etc.) works the stabilizers, and activates the entire core.

Additionally, it is one of the few horizontal pressing movements that allows the scapula to move naturally.  This is critical for function and shoulder health.  In this sense, the push-up is unlike any horizontal pressing exercise that requires you to lie on a bench.

Position #1 = Plank
Position #2 = Hovering Plank

Keep the body in a straight line.

Thanks Cathy!

TRICEPS
Overall, the triceps are probably the most important muscle in terms of upper body training. Biceps would be right up there as well.  Triceps make up 2/3 of the arm.  Strong triceps are necessary for every pushing movement and some pulling movements as well, where the arms are close to the body during the movement.

Triceps 'Dips' Use your own body-weight to work the back of the arms.  Keep the body close to the bench and bend the elbows back.  Thanks Lori! - Bend and stretch those arms!

Close Grip (narrow) Pushup

Stability Ball 'Skull Crusher'

Triceps 'Kickback'

Triceps Side Crunch

Triceps Overhead

Stability Ball Pushup (narrow)