Abstract: Lysine-specific demethylases 5 (KDM5) belong to the JMJD protein family and consist of JmjC, PHD, ARID and other characteristic domains. KDM5 can specifically remove the methyl groups of histone H3 lysine 4 (H3K4), and thus have been considered as potential therapeutic targets. To date, there have been reports of a large number of KDM5 inhibitors, some of which such as CPI-455 and EPT103182 have advanced into preclinical studies. In this review, we mainly focus on the recent progress on the protein structures and biological functions of KDM5 and their representative inhibitors, aiming to provide guidance for the structural design and optimization of novel KDM5 inhibitors.