 The most thoroughly worked-out theory of this type is the pilot wave theory developed by de Broglie and presented by him at the Fifth Solvay Conference held in Brussels in 1927, revived by David Bohm in 1952, and currently an active area of research by a small group of physicists and philosophers. According to this theory, there are particles with definite trajectories, that are guided by the quantum wave function. For the history of the de Broglie theory, see the introductory chapters of Bacciagaluppi and Valentini (2009). For an overview of the de Broglie-Bohm theory and philosophical issues associated with it see the entry on  Bohmian mechanics.