Safety is an important consideration in human-robot interactions. Robots can perform powerful movements that can cause hazards to humans surrounding them. To prevent accidents, it is important to identify sources of potential harm, to determine which of the persons in the robot’s vicinity may be in greatest peril and to assess the type of injuries the robot may cause to this person. This survey starts with a review of the safety issues in industrial settings, where robots manipulate dangerous tools and move with extreme rapidity and force. We then move to covering issues related to the growing numbers of autonomous mobile robots that operate in crowded (human-inhabited) environments. We discuss the potential benefits of fully autonomous cars on safety on roads and for pedestrians. Lastly, we cover safety issues related to assistive robots.