The service sector is the current technological frontier of automation, thanks to recent advanced in artificial intelligence and robotics, raising concerns for the future of work for a large segment of the workforce. This report surveys data on the variety and diffusion of service robots in the EU, in order to describe the state of automation in the service sector. Service robots are tangible artefacts of automation technology in the service sector and are relatively well defined by international standards, which makes it easier to track their diffusion. This report uses different data sources to show that the penetration of service robots is currently relatively low in the European economy, especially when compared to industrial robots. Moreover, service robots are used most often for manual tasks, in parts of the service sector that are most similar to manufacturing, such as logistics, inspection and maintenance, and surface cleaning. After comparing the different definitions and variety of service robots, this report proposes a general taxonomy for automation in the service sector, to guide future research.