Pullups require a combination of upper-body strength, coordination and practice to perfect your form and increase your reps. The main purpose of pullups is to increase the size and strength of your lats, biceps, triceps and the stabilizer muscles along your upper back and shoulders. Modifying your grip will get your chest involved in the exercise, but traditional pullups do not work your chest flexor muscles at all.
Pushups, punches and bench presses work your pectoralis major and anterior deltoids, the major muscles of your chest flexor, but pullups do not target these muscles, other than the pectoralis minor. The muscles of the chest are designed to act as pushing or lifting muscles; they also allow you to move your arms out in front of you and hold them in the center of your chest, but you don't need your major chest muscles for pulling or dragging.
The major muscles involved in traditional pullups are the lats, the broadest muscles in your back. Other muscles of the back that assist in the exercise include the lower and middle trapezius along with the levator scapulae and the rhomboids. In addition to these major back muscles, pullups work the stabilizer muscles of your shoulders and also target your arms.
Arms and Stabilizers
A firm grip is a necessity for proper pullups, but the muscles of your forearms, upper arms and the stabilizing muscles of your back and shoulders play an important role as well. Your biceps and triceps are the major muscles of your arms that are strained during pullups, while your posterior deltoids and the infraspinatus that run over your shoulder blades contract to keep you stable throughout your pull.
They aren't as common as traditional pullups and they don't work the muscles of your back quite as much, but underhand pullups -- sometimes called chinups -- work your biceps and triceps to a high degree and also get your chest muscles involved in the exercise. During chinups, your pectoralis major contracts along with your anterior deltoids and pectoralis minor, but they aren't going to give you the kind of chest definition that pushups or bench presses will.