Lysine-specific demethylase 1 (LSD1/KDM1A) has emerged as a promising target for the discovery of specific inhibitors as antitumor drugs. Based on the source of compounds, all LSD1 inhibitors in this review are divided into two categories: natural LSD1 inhibitors and synthetic LSD1 inhibitors. This review highlights the research progress of LSD1 inhibitors with the potential to treat cancer covering articles published in 2020. Design strategies, structure-activity relationships, co-crystal structure analysis and action mechanisms are also highlighted. Display omitted •LSD1 is a promising therapeutic target for cancer therapy.•LSD1 inhibitors published in 2020 are highlighted.•Co-crystal structures of representative LSD1/ inhibitors were highlighted.