Although push-ups are touted as an effective and convenient upper-body exercise, they don't work all the muscles in the upper body. Push-ups target the pressing muscles of the torso: the chest, shoulders and triceps. They do not target the back and biceps, which are the pulling muscles. The biceps are active to a small extent during push-ups, but their involvement is minimal and not enough to thoroughly work these arm muscles.
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During the push-up exercise, the short head of the biceps brachii muscle acts as a dynamic stabilizer. This means the muscle activates at both ends -- the elbow and the shoulder -- to help stabilize the joints. Although the biceps muscle is active, it does not change length to help generate the force needed to perform a push-up. Rather, it activates without changing length to counteract the forces of the triceps and to keep the elbow joint stable.
Because a push-up doesn't work the biceps through its full range of motion, you need to perform a pulling exercise in addition to the push-up movement. Incorporate compound back exercises, such as rows or pulldowns, and biceps isolation movements, such as curls, to target the biceps and other torso muscles not worked during push-ups.