In recent years, with the prosperity of big data and cloud computing, robotics is evolving from conventional networked robotics to internet-scale connected, big data driven, and cloud resources supercharged multi-robot systems. In this survey paper, we present a survey of an advancing, pioneering, and multi-disciplinary field of research at the intersection of wireless sensor networks (WSN), robotics and big data. We discuss the concepts of networked robots. Networked robots refer to multiple robots working together in coordination with different types of embedded computers, sensors, and human users. Networked robotics allows multiple robots and supporting entities to execute tasks that are well beyond the capabilities of a single robot. The recent initiation of cloud technologies is opening new prospects for the provisioning of advanced robotic services based on the cooperation of some connected robots, smart environments and devices powered by the huge computational and storage capability of the cloud servers. We have recently witnessed the emergence of cloud computing on one hand and robotics platforms on the other hand. These two areas have been merging and resulting in the cloud robotics model to offer more distant services. Since networked robots require high computational and processing power, big data is becoming a dominant factor in networked and cloud robotics. This survey paper elaborates the primary concepts of networked and cloud robotics, their applications, challenges as well as the importance of big data in robotics, particularly, networked and cloud robotics and the noteworthy works in these areas.