From April 3rd to April 8th 2005, a scientific workshop on the topic of ''Power-aware Computing Systems'' was held at Schloss Dagstuhl, Germany. The main seminar result is a classification of the obstacles, and therefore research directions, with respect to power consumption seen for different classes of devices, ranging from ultra low-power devices, over handheld devices, to servers and work stations. In a next step the seminar identified the impact different levels of dealing with power concerns can have. This paper summarises the objectives and structure as well as the outcome of that workshop.