The family of two-dimensional (2D) materials is comprised of a continually expanding palette of unique compositions and properties with potential applications in electronics, optoelectronics, energy capture and storage, catalysis, and nanomedicine. To accelerate the implementation of 2D materials in widely disseminated technologies, human health and environmental implications need to be addressed. While extensive research has focused on assessing the toxicity and environmental fate of graphene and related carbon nanomaterials, the potential hazards of other 2D materials have only recently begun to be explored. Herein, the toxicity and environmental fate of post-carbon 2D materials, such as transition metal dichalcogenides, hexagonal boron nitride, and black phosphorus, are reviewed as a function of their preparation methods and surface functionalization. Specifically, we delineate how the hazard potential of 2D materials is directly related to structural parameters and physicochemical properties, and how experimental design is critical to the accurate elucidation of the underlying toxicological mechanisms. Finally, a multidisciplinary approach for streamlining the hazard assessment of emerging 2D materials is outlined, thereby providing a pathway for accelerating their safe use in a range of technologically relevant contexts.