The Edge computing paradigm has gained prominence in both academic and industry circles in recent years. By implementing edge computing facilities and services in robotics, it becomes a key enabler in the deployment of artificial intelligence applications to robots. Time-sensitive robotics applications benefit from the reduced latency, mobility, and location awareness provided by the edge computing paradigm, which enables real-time data processing and intelligence at the network's edge. While the advantages of integrating edge computing into robotics are numerous, there has been no recent survey that comprehensively examines these benefits. This paper aims to bridge that gap by highlighting important work in the domain of edge robotics, examining recent advancements, and offering deeper insight into the challenges and motivations behind both current and emerging solutions. In particular, this article provides a comprehensive evaluation of recent developments in edge robotics, with an emphasis on fundamental applications, providing in-depth analysis of the key motivations, challenges, and future directions in this rapidly evolving domain. It also explores the importance of edge computing in real-world robotics scenarios where rapid response times are critical. Finally, the paper outlines various open research challenges in the field of edge robotics.