Cell cycle checkpoints act to protect cells from external stresses and internal errors that would compromise the integrity of the cell. Checkpoints are often defective in cancer cells. Drugs that target checkpoint mechanisms should therefore be selective for tumor cells that are defective for the drug‐sensitive checkpoint. Histone deacetylase inhibitors typify this class of agents. They trigger a G₂‐phase checkpoint response in normal cells but are cytotoxic in tumor cells in which this checkpoint is defective. In this study, we investigated the molecular basis of the tumor‐selective cytotoxicity of these drugs and demonstrated that it is due to the disruption of two cell cycle checkpoints. The first is the histone deacetylase inhibitor‐sensitive G₂‐phase checkpoint, which is defective in drug‐sensitive cells and permits cells to enter an aberrant mitosis. The second is the drug‐dependent bypass of the mitotic spindle checkpoint that normally detects aberrant mitosis and blocks mitotic exit until the defect is rectified. The disruption of both checkpoints results in the premature exit of cells from an abortive mitosis followed by apoptosis. This study of histone deacetylase inhibitors demonstrates that drugs targeting cell cycle checkpoints can provide the selectivity and cytotoxicity desired in effective chemotherapeutic agents.