As a result of the difficulties brought by COVID-19 and its associated lockdowns, many individuals and companies have turned to robots in order to overcome the challenges of the pandemic. Compared with traditional human labor, robotic and autonomous systems have advantages such as an intrinsic immunity to the virus and an inability for human-robot-human spread of any disease-causing pathogens, though there are still many technical hurdles for the robotics industry to overcome. This survey comprehensively reviews over 200 reports covering robotic systems which have emerged or have been repurposed during the past several months, to provide insights to both academia and industry. In each chapter, we cover both the advantages and the challenges for each robot, finding that robotics systems are overall apt solutions for dealing with many of the problems brought on by COVID-19, including: diagnosis, screening, disinfection, surgery, telehealth, care, logistics, manufacturing and broader interpersonal problems unique to the lockdowns of the pandemic. By discussing the potential new robot capabilities and fields they applied to, we expect the robotics industry to take a leap forward due to this unexpected pandemic.