In recent years, commercial and research interest in service robots working in everyday environments has grown. These devices are expected to move autonomously in crowded environments, maximizing not only movement efficiency and safety parameters, but also social acceptability. Extending traditional path planning modules with socially aware criteria, while maintaining fast algorithms capable of reacting to human behavior without causing discomfort, can be a complex challenge. Solving this challenge has involved the development of proactive systems that take into account cooperation (and not only interaction) with the people around them, the determined incorporation of approaches based on Deep Learning, or the recent fusion with skills coming from the field of human–robot interaction (speech, touch). This review analyzes approaches to socially aware navigation and classifies them according to the strategies followed by the robot to manage interaction (or cooperation) with humans.