Bromodomains are epigenetic readers of histone acetylation involved in chromatin remodeling and transcriptional regulation. The human proteome comprises 46 bromodomain-containing proteins with a total of 61 bromodomains, which, despite highly conserved structural features, recognize a wide array of natural peptide ligands. Over the past five years, bromodomains have attracted great interest as promising new epigenetic targets for diverse human diseases, including inflammation, cancer, and cardiovascular disease. The demonstration in 2010 that two small molecule compounds, JQ1 and I-BET762, potently inhibit proteins of the bromodomain and extra-terminal (BET) family with translational potential for cancer and inflammatory disease sparked intense efforts in academia and pharmaceutical industry to develop novel bromodomain antagonists for therapeutic applications. Several BET inhibitors are already in clinical trials for hematological malignancies, solid tumors and cardiovascular disease. Currently, the field faces the challenge of single-target selectivity, especially within the BET family, and of overcoming problems related to the development of drug resistance. At the same time, new trends in bromodomain inhibitor research are emerging, including an increased interest in non-BET bromodomains and a focus on drug synergy with established antitumor agents to improve chemotherapeutic efficacy. This review presents an updated view of the structure and function of bromodomains, traces the development of bromodomain inhibitors and their potential therapeutic applications, and surveys the current challenges and future directions of this vibrant new field in drug discovery.