This CBMS-2012 keynote first outlines standard approaches to data mining, with the emphasis on subgroup discovery which proves to be an effective tool for data analysis in biomedical applications. The core of this paper is devoted to inductive logic programming and relational data mining which also have a great potential for biomedical research, with a focus on recently developed approaches to semantic data mining which enable the use of domain ontologies as background knowledge in data analysis. The use of described techniques and tools is illustrated on selected biomedical applications.