Plutonium and plutonium-based alloys containing Al or Ga exhibit numerous phases with crystal structures ranging from simple monoclinic to face-centered cubic. Only recently, however, has there been increased convergence in the actinides community on the details of the equilibrium form of the phase diagrams. Practically speaking, while the phase diagrams that represent the stability of the fcc delta-phase field at room temperature are generally applicable, it is also recognized that Pu and its alloys are never truly in thermodynamic equilibrium because of self-irradiation effects, primarily from the alpha decay of Pu isotopes. This article covers past and current research on several properties of Pu and Pu-(Al or Ga) alloys and their connections to the crystal structure and the microstructure. We review the consequences of radioactive decay, the recent advances in understanding the electronic structure, the current research on phase transformations and their relations to phase diagrams and phase stability, the nature of the isothermal martensitic delta -> alpha' transformation, and the pressure-induced transformations in the delta-phase alloys. New data are also presented on the structures and phase transformations observed in these materials following the application of pressure, including the formation of transition phases. (C) 2009 Elsevier Ltd. All rights reserved.