The capability of a mobile robot to efficiently and safely perform complex missions is limited by its knowledge of the environment, namely the situation. Advanced reasoning, decision-making, and execution skills enable an intelligent agent to act autonomously in unknown environments. Situational Awareness (SA) is a fundamental capability of humans that has been deeply studied in various fields, such as psychology, military, aerospace, and education. Nevertheless, it has yet to be considered in robotics, which has focused on single compartmentalized concepts such as sensing, spatial perception, sensor fusion, state estimation, and Simultaneous Localization and Mapping (SLAM). Hence, the present research aims to connect the broad multidisciplinary existing knowledge to pave the way for a complete SA system for mobile robotics that we deem paramount for autonomy. To this aim, we define the principal components to structure a robotic SA and their area of competence. Accordingly, this paper investigates each aspect of SA, surveying the state-of-the-art robotics algorithms that cover them, and discusses their current limitations. Remarkably, essential aspects of SA are still immature since the current algorithmic development restricts their performance to only specific environments. Nevertheless, Artificial Intelligence (AI), particularly Deep Learning (DL), has brought new methods to bridge the gap that maintains these fields apart from the deployment to real-world scenarios. Furthermore, an opportunity has been discovered to interconnect the vastly fragmented space of robotic comprehension algorithms through the mechanism of Situational Graph (S-Graph), a generalization of the well-known scene graph. Therefore, we finally shape our vision for the future of robotic Situational Awareness by discussing interesting recent research directions.