Anthropomorphic service robots are on the rise. The more capable they become and the more regular they are applied in real-world settings, the more critical becomes the responsible design of human-robot interaction (HRI) with special attention to human dignity, transparency, privacy, and robot compliance. In this paper we review the interdisciplinary state of the art relevant for the responsible design of HRI. Furthermore, directions for future research on the responsible design of HRI with anthropomorphic service robots are suggested.