|Ensuring human safety is one of the most important considerations within the field of human-robot interaction (HRI). This does not simply involve preventing collisions between humans and robots operating within a shared space; we must consider all possible ways in which harm could come to a person, ranging from physical contact to adverse psychological effects resulting from unpleasant or dangerous interaction. In this work, we define what safe HRI entails and present a survey of potential methods of ensuring safety during HRI. We classify this collection of work into four major categories: safety through control, motion planning, prediction, and consideration of psychological factors. We discuss recent work in each major category, identify various sub-categories and discuss how these methods can be utilized to improve HRI safety. We then discuss gaps in the current literature and suggest future directions for additional work. By creating an organized categorization of the field, we hope to support future research and the development of new technologies for safe HRI, as well as facilitate the use of these techniques by researchers within the HRI community.