The Cloud infrastructure and its extensive set of Internet-accessible resources has potential to provide significant benefits to robots and automation systems. We consider robots and automation systems that rely on data or code from a network to support their operation, i.e., where not all sensing, computation, and memory is integrated into a standalone system. This survey is organized around four potential benefits of the Cloud: 1) Big Data: access to libraries of images, maps, trajectories, and descriptive data; 2) Cloud Computing: access to parallel grid computing on demand for statistical analysis, learning, and motion planning; 3) Collective Robot Learning: robots sharing trajectories, control policies, and outcomes; and 4) Human Computation: use of crowdsourcing to tap human skills for analyzing images and video, classification, learning, and error recovery. The Cloud can also improve robots and automation systems by providing access to: a) datasets, publications, models, benchmarks, and simulation tools; b) open competitions for designs and systems; and c) open-source software. This survey includes over 150 references on results and open challenges. A website with new developments and updates is available at: http://goldberg.berkeley.edu/cloud-robotics/ Note to Practitioners-Most robots and automation systems still operate independently using onboard computation, memory, and programming. Emerging advances and the increasing availability of networking in the "Cloud" suggests new approaches where processing is performed remotely with access to dynamic global datasets to support a range of functions. This paper surveys research to date.