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The human shoulder plays an important role in human posture and motion, especially in scenarios in which humans need achieve tasks with external loads. The shoulder complex model is critical in digital human modeling and simulation because a fidelity model is the basis for realistic posture and motion predictions for digital humans. The complexity of the shoulder mechanism makes it difficult to model a shoulder complex realistically. Although many researchers have attempted to model the human shoulder complex, there has not been a survey of these models and their benefits and limitations. This paper attempts to review various biomechanical models proposed and summarize the pros and cons. It focuses mainly on the human modeling domain, although some of these models were originally from the robotics field. The models are divided into two major categories: open-loop chain models and closed-loop chain models.