The evolution of reverse total shoulder arthroplasty (rTSA) is presented from a prosthesis design perspective along with the results of a design optimization analysis in which 32 different geometric iterations of the Grammont reverse shoulder were evaluated to identify parameters that minimize scapular impingement while maximizing range of motion and stability. Specifically, humeral neck angle, humeral stem/liner offset, humeral liner constraint, glenosphere diameter, glenosphere thickness, position of the center of rotation, and glenoid baseplate design characteristics are each discussed, with optimized recommendations for each presented. Additionally, we propose a rTSA prosthesis design classification system to objectively identify and categorize different designs based upon glenoid or humeral prosthesis characteristics for the purpose of helping the surgeon determine which design configuration best suits a given clinical scenario. The impact of each prosthesis classification type on shoulder muscle length, deltoid wrapping, and muscle moment arms are also described to illustrate how each prosthesis classification type impacts these biomechanical parameters. Finally, clinical outcomes with one particular optimized prosthesis design are presented along with evolving applications of rTSA, including its use in eroded glenoid morphologies, the implications of subscapularis repair, the role of muscle transfers.