Intense visible upconversion luminescence is observed in a Re4+-doped low-phonon host material, Cs2ZrCl6, with excitation in the near-infrared. The upconversion excitation wavelength, temperature, power, and time dependence is studied using variable-temperature absorption and luminescence spectroscopies, and modeled using a three-level set of coupled nonlinear rate equations. On the basis of analysis of these data, energy-transfer upconversion is shown to be the dominant mechanism responsible for this phenomenon. The main properties of this upconversion mechanism are correlated to properties of the Re4+ electronic structure, in particular the large energy gaps, the small excited-state distortions, and the lack of cross-relaxation pathways for radiationless decay. These properties make this ion attractive for upconversion phosphor and laser materials applications, and two potential upconversion laser schemes are proposed. The contributions of these same properties to the photoredox chemistry of Re4+ and related d(3) ions are discussed.