Navigation lies at the core of social robotics, enabling robots to navigate and interact seamlessly in human environments. The primary focus of human-aware robot navigation is minimizing discomfort among surrounding humans. Our review explores user studies, examining factors that cause human discomfort, to perform the grounding of social robot navigation requirements and to form a taxonomy of elementary necessities that should be implemented by comprehensive algorithms. This survey also discusses human-aware navigation from an algorithmic perspective, reviewing the perception and motion planning methods integral to social navigation. Additionally, the review investigates different types of studies and tools facilitating the evaluation of social robot navigation approaches, namely datasets, simulators, and benchmarks. Our survey also identifies the main challenges of human-aware navigation, highlighting the essential future work perspectives. This work stands out from other review papers, as it not only investigates the variety of methods for implementing human awareness in robot control systems but also classifies the approaches according to the grounded requirements regarded in their objectives.