In 1957, Löwdin presented an overview of various methods used in molecular and solid-state theory for the solution of the Schrödinger equation in his account. Amazingly, most of the principles and hierarchy set out in that overview prevailed until the present time. Propelled by developments in other fields (most notably the design and construction of efficient and affordable computer hardware), a huge part of Dirac's and Löwdin's programs set for future generations has become a reality.