The lysine-specific demethylase (LSD1) is a flavin-dependent amine oxidase that selectively removes one or two methyl groups from histone H3 at the Lys4 position. Along with histone deacetylases 1 and 2, LSD1 is involved in epigenetically silencing gene expression. LSD1 has been implicated as a potential therapeutic target in cancer and other diseases. In this chapter, we discuss several approaches to measure LSD1 demethylase activity and their relative strengths and limitations for inhibitor discovery and mechanistic characterization. In addition, we review the principal established chemical functional groups derived from monoamine oxidase inhibitors that have been investigated in the context of LSD1 as demethylase inhibitors. Finally, we highlight a few examples of recently developed LSD1 mechanism-based inactivators and their biomedical applications.