• The HDAC inhibitor suberic bishydroxamate (SBHA) upregulated Bim, Bax and Bak in human melanoma cells.• The HDAC inhibitor Trichostatin A restored histone acetylation, with concomitant upregulation of Bim.• Trichostatin A suppressed miR-106b∼93∼25 expression through downregulation of c-Myc, thereby increasing Bim expression and apoptosis in human endometrial cancer cells.• The HDAC inhibitor vorinostat increased Bim expression and sensitized EGFR-mutant non-small-cell lung cancer (NSCLC) to the tyrosine kinase inhibitor gefitinib. This evidence concerns the gene HDAC9 and non-small cell lung carcinoma.