•Perception, cognition and control methods for safe human robot interaction.•Safe hardware and software development, low level admittance controller.•Human aware navigation, virtual collaborative zones.•Psychological factors in human robot interaction.•Robot safety features chronological map.•Systems’ theoretic analysis. In the era of industrialization and automation, safety is a critical factor that should be considered during the design and realization of each new system that targets operation in close collaboration with humans. Of such systems are considered personal and professional service robots which collaborate and interact with humans at diverse applications environments. In this collaboration, human safety is an important factor in the wider field of human-robot interaction (HRI) since it facilitates their harmonic coexistence. The paper at hand aims to systemize the recent literature by describing the required levels of safety during human-robot interaction, focusing on the core functions of the collaborative robots when performing specific processes. It is also oriented towards the existing methods for psychological safety during human-robot collaboration and its impact at the robot behaviour, while also discusses in depth the psychological parameters of robots incorporation in industrial and social environments. Based on the existing works on safety features that minimize the risk of HRI, a classification of the existing works into five major categories namely, Robot Perceptions for Safe HRI, Cognition-enabled robot control in HRI, Action Planning for safe navigation close to humans, Hardware safety features, and Societal and Psychological factors is also applied. Finally, the current study further discusses the existing risk assessment techniques as methods to offer additional safety in robotic systems presenting thus a holistic analysis of the safety in contemporary robots, and proposes a roadmap for safety compliance features during the development of a robotic system.