Hafnium oxide plays an important role as a dielectric material in various thin-film electronic devices such as transistors and resistive or ferroelectric memory. The crystallographic and electronic structure of the hafnia layer often depends critically on its composition and defect structure. Here, we report two novel defect-stabilized polymorphs of substoichiometric HfO_2–x with semiconducting properties that are of particular interest for resistive switching digital or analog memory devices. The thin-film samples are synthesized by molecular beam epitaxy with oxygen engineering that allows us to cover the whole range of metallic Hf with oxygen interstitials to HfO₂. The crystal and defect structures, in particular of a cubic low-temperature phase c-HfO_1.7 and a hexagonal phase hcp-HfO_0.7 are identified by X-ray diffraction, in vacuo electron spectroscopic, and transmission electron microscopic methods. With the help of UV/Vis transmission data, we propose a consistent band structure model for the whole oxidation range involving oxygen vacancy-induced in-gap defect states. Our comprehensive study of engineered hafnia thin films has an impact on the design of resistive memory devices and can be transferred to chemically similar suboxide systems.