Captured element shoulder joint implant may be configured with a captured humeral ball; in a reverse shoulder configuration; to have a barrel- or disc-like humeral head to recessed glenoid articulation; and so forth. Multi-point fixation glenoid component may be provided. A humeral implant may have a universal joint connection, which can be mounted to or in a humeral bone and provide for a center of movement generally within a volume defined by an upper head of a normal humerus.