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Tungsten diselenide (WSe₂) is being actively pursued for two-dimensional electronics and as a host for single-photon emitters. We have studied the properties of native defects and impurities in WSe₂ using density functional theory with a hybrid functional. We find that all native defects give rise to levels that are deep in the band gap, and thus will not contribute to conductivity. The defect chemistry of WSe₂ is likely dominated by common background impurities. In particular, substitutional oxygen, carbon, and transition metal impurities such as vanadium, are low energy defects. Our results allow us to comment on the origin of the frequently observed p-type conductivity and sub-band gap emission lines in as-grown WSe₂