Angles of the shoulder joint are usually defined in each of the sagittal, coronal, and horizontal planes passing through the center of the shoulder joint. One of the problems with this method is the difficulty of describing some positions of the shoulder joint such as the anterolaterally elevated position. In 2005, the International Society of Biomechanics proposed a recommendation on definitions of joint coordinate systems including the shoulder based on Euler/Cardan angles, which have often been used for the purpose of research on shoulder joint movement in daily activities. With this definition, however, it still remains impossible to define the angle of axial rotation in the hanging down position. Also, Codman's paradox, the phenomenon where the rotation angle of the shoulder changes after motions without axial rotation of the arm, remains unsolved. To solve these problems, a new method to define the angle of shoulder axial rotation, the non-singular method, has been proposed. This review describes the history and the problems of the methods used to define shoulder angles, and presents this new method of definition.