Rotator cuff (RC) disease is an extremely common condition associated with shoulder pain, reduced functional capacities and impaired quality of life. It primarily involves alterations in tendon health and mechanical properties that can ultimately lead to tendon failure. RC tendon tears induce progressive muscular changes that negatively impact surgical reparability of the RC tendons and clinical outcomes. At the same time, a significant base of clinical data suggests a relatively weak relationship between RC integrity and clinical presentation, emphasizing the multifactorial aspects of RC disease. This review aims to summarize the potential contribution of peripheral, spinal and supraspinal neural factors that may: (i) exacerbate structural and functional muscle changes induced by tendon tear, (ii) compromise the reversal of these changes during surgery and rehabilitation, (iii) contribute to pain generation and persistence of pain, iv) impair shoulder function through reduced proprioception, kinematics and muscle recruitment, and iv) help to explain interindividual differences and response to treatment. Given the current clinical and scientific interest in peripheral nerve injury in the context of RC disease and surgery, we carefully reviewed this body of literature with a particular emphasis for suprascapular neuropathy that has generated a large number of studies in the past decade. Within this process, we highlight the gaps in current knowledge and suggest research avenues for scientists and clinicians.