The mechanical performance—including deformation, fracture, and radiation damage—of zirconium is determined at the atomic scale. With Zr and its alloys extensively used in the nuclear industry, understanding that atomic-scale behavior is crucial. The defects controlling that performance are at size scales far larger than accessible by first-principles methods, necessitating the use of semi-empirical interatomic potentials. Existing potentials for Zr are not sufficiently quantitative, nor easily extendable to alloys, oxides, or hydrides. To overcome these issues, a neural network machine learning potential (NNP) is developed here within the Behler-Parrinello framework for Zr. With a careful choice of descriptors of the atomic environments and the creation of a first-principles training dataset that includes a wide spectrum of configurations of metallurgical relevance, a very accurate NNP is demonstrated. Specifically, the Zr NNP yields a good description of dislocation structures and their relative energies and fracture behavior, along with bulk, surface, and point-defect properties and structures, and significantly outperforms the best available traditional potentials. Results here will enable large-scale simulations of complex processes and provide the basis for future extensions to alloys, oxides, and hydrides.