The key management of glenohumeral osteoarthritis is shoulder arthroplasty which aims to reduce pain and restore full shoulder function: it has increased in recent years. A detailed understanding of the anatomy of the glenoid and humeral head, as well as morphological changes of the glenoid in osteoarthritis, are important factors to consider when deciding on replacement components. This review begins with a brief introduction of the glenohumeral joint itself, and then considers the detailed anatomy of the glenoid fossa and humeral head, both of which are reported to have variable morphology. Several studies have been undertaken to assess various parameters, especially of the glenoid fossa including its shape, height, width, and articular surface area, version and inclination, in an attempt to define a standard classification that can be applied to surgical intervention. Nevertheless, no definitive consensus concerning the classification of these morphologies has been forthcoming, hence the need for this review. Following a consideration of these morphologies, the current state of knowledge regarding glenoid deformity in osteoarthritis, as well as its surgical management, is considered.