I review the principal theories that have been proposed for the superconducting phases of UPt3. The detailed H-T phase diagram places constraints on any theory for the multiplesupercond cting phases. Much attention has been given to the Ginzburg-Landau (GL) region of the phase diagram where the phase boundaries of three phases appear to meet at a tetracritical point. I has been argued that the existence of a tetracritical point for all field orientations eliminates the two-dimensional (2D) orbital representations coupled to a symmetry breaking field (SBF) as viable theory of these phases, and favors either (i) a theory based on two primary order parameters belonging to different irreducible representations that are accidentally degenerate [Chen and Garg, Phys. Rev. Lett. 70, 1689 (1993)], or (ii) a spin-triplet, orbital one-dimensional (1D) representation with no spin-orbit coupling in the pairing channel [Machida and Ozaki, Phys. Rev. Lett. 66, 3293 (1991)]. I comment on the limitations of the models proposed so far for the superconducting phases of UPt3. I also find that a theory in which the order parameter belongs to an orbital 2D representation coupled to a SBF is a viable model for the phases of UPt3, based on the existing body of experimental data. Specifically, I show that (1) the existing phase diagram (including an apparent tetracritical point for all field orientations), (2) the anisotropy of the upper critical field over the full temperature range, (3) the correlation between superconductivity and basal plane antiferromagnetism and (4) low-temperature power laws in the transport and thermodynamic properties can be explained qualitatively, and in many respects quantitatively, by an odd-parity, E2u order parameter with a pair spin projection of zero along the c-axis. The coupling of an AFM moment to the superconducting order parameter acts as a symmetry breaking field (SBF) which is responsible for the apparent tetracritical point, in addition to the zero-field double transition. The new results presented here for the E2u representation are based on an analysis of the material parameters calculated within BCS theory for the 2D representations, and a refinement of the SBF model of Hess, et al. [J. Phys. Condens. Matter, 1, 8135 (1989)]. I also discuss possible experiments to test the symmetry of the order parameter.