Lysine-specific demethylase 1 (LSD1), the first identified histone demethylase, was belonged to the superfamily of the flavin adenine dinucleotide (FAD)-dependent amine oxidases. LSD1 specifically demethylates mono- or dimethylated dimethylated histone H3 lysine4 (H3K4) and H3 lysine 9 (H3K9) via a redox process. Recently evidences showed that LSD1 played an important role in a broad spectrum of biological processes, including cell proliferation, adipogenesis, spermatogenesis, chromosome segregation and embryonic development. Furthermore, LSD1 also could promote progress of tumor by inhibiting the tumor suppressor activity of p53. To date, as a potential drug for discovering anti-tumor drugs, the medical significance of LSD1 inhibitors have been greatly appreciated. Here, we reviewed the remarkable progress being made in understanding of LSD1, mainly on its structure, basic function and medical application in tumor therapy.