HfO2 shows different polymorphs, including monoclinic and orthorhombic ones, that exhibit singular properties. Moreover, the character of HfO2 is also influenced by the Zr atoms as a doping agent. Here, an extensive study of the monoclinic P21/c and the orthorhombic Pca21 polymorphs of HfO2, Hf0.75Zr0.25O2, and Hf0.5Zr0.5O2 is reported. For all six systems, density functional theory (DFT) methods based on generalized gradient approximations (GGAs) were first used; then the GGA + U method was settled and calibrated to describe the electrical and optical properties of polymorphs and the responses to the oxygen vacancies. Zr had different effects in relation to the polymorph; moreover, the amount of Zr led to important differences in the optical properties of the Pca21 polymorph. Finally, oxygen vacancies were investigated, showing an important modulation of the properties of HfxZryO2 nanostructures. The combined GGA and GGA + U methods adopted in this work generate a reasonable prediction of the physicochemical properties of o- and m-HfxZryO2, identifying the effects of doping phenomena.