Reverse shoulder arthroplasty (RSA) has become a widely used procedure since its introduction in the 1980s, and is currently used to treat a wider range of conditions than its original indication. The original Grammont-style RSA revolutionized shoulder arthroplasty but had several limitations, including scapular notching and reduced rotational motion. This review discusses the evolution of RSA design, particularly the development of a lateralized center of rotation constructs, which aims to improve all the disadvantages associated with the Grammont-style design and more closely reproduce the native anatomy in order to improve patient outcomes in an expanded context of pathologies.