Long-lived radioactive isotopes produced by cosmogenic activation can be a major source of background for rare event searches such as dark matter and neutrinoless double beta decay. In this talk, I will present measurements of cosmogenic production rates in active detector materials, including argon, silicon, and sodium iodide; a method to track the cosmic-ray exposure of detector components using selected witness materials; and a technique for efficiently removing cosmogenic tritium from high-purity silicon.