The main muscles of the chest are called pectorals. There are two muscles that make the pectorals, pectoralis major and pectoralis minor. Pec major is the larger muscle that originates from the sternum and upper ribs and inserts to the upper arm bone. The pec minor is smaller and lies deep to the pec major, it originates from the upper ribs and inserts into the top of the shoulder blade.
Both muscles can become tight for many reasons. Excessive push exercise, such as pushups and bench press often contribute. A slouched posture can also result in a muscle imbalance which pulls the shoulders forward leading to potential pec tightness.
Patients will often present with pec tightness. In a lot of these cases stretching may be beneficial. Because each of these muscles has different insertion points as well as actions, they must be stretched differently.