The paper attempts to derive directions for research and teaching in health informatics. To this end, the achievements and continuing challenges of health informatics are exemplified, categorized, and related to common underlying phenomena. Suggestions by Blum and Blois are adopted which point to the complexity of health information as the critical ingredient. Examples are given of current efforts directed at dealing with this complexity. According to Popper and Brookes one may have to search for yet other ways of dealing specifically with information; we have barely started to explore these. It is suggested that this requirement for a fundamentally different orientation has profound consequences not only for our research but also for our teaching.