In this review, we provide a summary of recent progress in ontology mapping (OM) at a crucial time when biomedical research is under a deluge of an increasing amount and variety of data. This is particularly important for realising the full potential of semantically enabled or enriched applications and for meaningful insights, such as drug discovery, using machine-learning technologies. We discuss challenges and solutions for better ontology mappings, as well as how to select ontologies before their application. In addition, we describe tools and algorithms for ontology mapping, including evaluation of tool capability and quality of mappings. Finally, we outline the requirements for an ontology mapping service (OMS) and the progress being made towards implementation of such sustainable services.