Ten major long-term aims and tasks, so to speak 'grand challenges', for research in the field of medical informatics, including health informatics, are proposed and described. These are the further development of methods and tools of information processing for: (1) diagnostics ('the visible body'); (2) therapy ('medical intervention with as little strain on the patient as possible'); (3) therapy simulation; (4) early-recognition and prevention; (5) compensating physical handicaps; (6) health consulting ('the informed patient'); (7) health reporting; (8) health care information systems; (9) medical documentation and (10) comprehensive documentation of medical knowledge and knowledge-based decision support. Work is, in part, already in progress. To all these aims and tasks medical informatics can and may be should make substantial contributions. Prior to outlining the above aims and tasks, an account is given of the meaning of medical informatics, of the objective it pursues in general and of its achievements so far. The present paper intends to contribute to a broad public discussion of the aims and tasks for research in the field of medical informatics.