Histone deacetylases (HDACs) are essential for maintaining homeostasis by catalyzing histone deacetylation. Aberrant expression of HDACs is associated with various human diseases. Although HDAC inhibitors are used as effective chemotherapeutic agents in clinical practice, their applications remain limited due to associated side effects induced by weak isoform selectivity. HDAC1 displays unique structure and cellular localization as well as diverse substrates and exhibits a wider range of biological functions than other isoforms. HDAC1 displays a unique structure primarily found in the nucleus and involved in epigenetic and transcriptional regulation. HDAC1 is ubiquitously expressed and associated with Sin3, NuRD, and CoRest transcription repressive complexes responsible for distinct cellular processes like cell proliferation and survival. HDAC1 inhibitors have been effectively used to treat various cancers such as gastric, breast, colorectal, prostate, colon, lung, ovarian, pancreatic, and inflammation without exerting significant toxic effects. In this review, we summarize four major structural classes of HDAC1 inhibitors (i.e., hydroxamic acid derivatives, benzamides, hydrazides, and thiols) with their structural activity relationship. This review is a comprehensive work on HDAC1 inhibitors to achieve deep insight of knowledge about the structural information of HDAC1 inhibitors. It may provide up-to-date direction for developing new selective HDAC1 inhibitors as anticancer agents.