Service science is still in a formative stage, with many basic ideas still in flux and significant disagreements about definitions and implications of basic concepts. This paper suggests directions for progress in relation to eight problematic areas within service science. It uses five typical medical services to question typical definitions of service and service system. It suggests that service science should not privilege servitizing over productizing; that a series of design dimensions whose end-points are often associated with products or with services are more useful than yes/no distinctions between products and services; that the concept of "the customer" should be replaced with clearer identification of different groups and types of customers; that value co-production by customers and co-creation by providers are optional characteristics of services; that assumptions about the importance of the intentions and variability of service system participants should be clarified;. and that better balance between analytical rigor and the spirit of service is often needed. As a starting point for addressing these challenges, the concluding section identifies premises underlying an integrated view of service marketing, service operations, and service computing.