Robots come into physical contact with humans in both experimental and operational settings. Many potential factors motivate the detection of human contact, ranging from safe robot operation around humans, to robot behaviors that depend on human guidance. This article presents a review of current research within the field of Tactile Human-Robot Interactions (Tactile HRI), where physical contact from a human is detected by a robot during the execution or development of robot behaviors. Approaches are presented from two viewpoints: the types of physical interactions that occur between the human and robot, and the types of sensors used to detect these interactions. We contribute a structure for the categorization of Tactile HRI research within each viewpoint. Tactile sensing techniques are grouped into three categories, according to what covers the sensors: (i) a hard shell, (ii) a flexible substrate or (iii) no covering. Three categories of physical HRI likewise are identified, consisting of contact that (i) interferes with robot behavior execution, (ii) contributes to behavior execution and (iii) contributes to behavior development. We populate each category with the current literature, and furthermore identify the state-of-the-art within categories and promising areas for future research.