Cloud infrastructure and its extensive set of Internet-enabled resources have the potential to provide significant benefits to robots and flexible systems. We look for robots and data-switching programs or code from the network to support their performance, that is, when not all sense, calculation, and memory are integrated into the standalone system. This survey is designed for four possible Cloud benefits: 1) Big Data: access to photo libraries, maps, trajectories, and descriptive data; 2) Cloud Computing: access to the same grid computer with the demand for mathematical analysis, reading, and movement planning; 3) Integrated Robots Learning: robots that share tracking, control policies, and results; and 4) Census: use of crowdourcing to tap people's skills for image and video analysis, classification, reading, and error retrieval. The cloud can also improve robots and flexible systems by providing access to: a) data sets, publications, models, measurements, and simulation tools; b) open competitions for designs and programs; and c) open source software.