The service sector – which includes government, education, medical and healthcare, banking and insurance, consulting, information technology services, retail and wholesale, tourism and hospitality, entertainment, transportation and logistics, and legal among others – accounts for most of the world’s economic activity, but is the least studied and least understood part of the economy. Innovation in service in particular is not approached as systematically as innovation in agriculture and manufacturing, which have experienced large productivity and quality gains in the last two hundred years. To remedy this, we propose developing a science of service, which aims to provide theory and practice around service innovation. In this paper, we show progress toward this, arguing that the proper basic category is the service system in which entities exchange performance of beneficial action, and that a service system can be understood as a system composed of people and technologies that adaptively computes and adjusts to the changing value of knowledge in the system.