Cathode materials with structure similar to the mineral tavorite have shown promise for use in lithium-ion batteries, but this class of materials is relatively unexplored. We use high-throughput density-functional-theory calculations to evaluate tavorite-structured oxyphosphates, fluorophosphates, oxysulfates, and fluorosulfates for use as cathode materials in lithium-ion batteries. For each material we consider the insertion of both one and two lithium ions per redox-active metal, calculating average voltages and stability relative to a database of nearly 100,000 previously calculated compounds. To evaluate lithium mobility, we calculate the activation energies for lithium diffusion through the known tavorite cathode materials LiVO(PO4), LiV(PO4)F, and LiFe(SO4)F. Our calculations indicate that tavorite-structured materials are capable of very high rates of one-dimensional lithium diffusion, and several tavorite-structured materials may be capable of reversibly inserting two lithium ions per redox-active metal.Keywords: lithium-ion battery; cathode material; tavorite; density functional theory; high-throughput; computational