Lysine-specific demethylase 1A (LSD1, also named KDM1A) is a demethylase that can remove methyl groups from histones H3K4me1/2 and H3K9me1/2. It is aberrantly expressed in many cancers, where it impedes differentiation and contributes to cancer cell proliferation, cell metastasis and invasiveness, and is associated with inferior prognosis. Pharmacological inhibition of LSD1 has been reported to significantly attenuate tumor progression in vitro and in vivo in a range of solid tumors and acute myeloid leukemia. This review will present the structural aspects of LSD1, its role in carcinogenesis, a comparison of currently available approaches for screening LSD1 inhibitors, a classification of LSD1 inhibitors, and its potential as a drug target in cancer therapy.