End spaces of infinite graphs sit at the interface between graph theory, group theory and topology. They arise as the boundary of an infinite graph in a standard sense generalising the theory of the Freudenthal boundary developed by Freudenthal and Hopf in the 1940's for infinite groups.A long-standing quest in infinite graph theory with a rich body of literature seeks to describe the possible end structures of graphs by a set of low-complexity representatives. In this paper we present a solution to this fifty-year-old problem by showing that every end space is homeomorphic to the end space of some (uniform graph on a) special order tree.