In this survey, we review the field of human shoulder functional kinematic representations. The central question of this review is to evaluate whether the current approaches in shoulder kinematics can meet the high-reliability computational challenge. This challenge is posed by applications such as robot-assisted rehabilitation. Currently, the role of kinematic representations in such applications has been mostly overlooked. Therefore, we have systematically searched and summarised the existing literature on shoulder kinematics. The shoulder is an important functional joint, and its large range of motion (ROM) poses several mathematical and practical challenges. Frequently, in kinematic analysis, the role of the shoulder articulation is approximated to a ball-and-socket joint. Following the high-reliability computational challenge, our review challenges this inappropriate use of reductionism. Therefore, we propose that this challenge could be met by kinematic representations, that are redundant, that use an active interpretation and that emphasise on functional understanding.