Over the last decade, digitization and individualization have fostered the development of on-demand services in many industries. In the insurance sector, technological progress brings new possibilities on how risks can be insured. This paper studies on-demand insurance and thereby takes three perspectives. First, we define on-demand insurance and study the current market landscape of offerings leading to a characterization of the phenomenon. Second, we analyze the on-demand insurance business model, discuss how value is created, and develop a taxonomy of the dimensions among business model components. Third, we describe the awareness and interest of potential customers in Switzerland using novel data recorded from a recent consumer survey. Using the results from the market study, business model analysis, and customer survey, we discuss the (future) role of on-demand insurance shedding light on the ongoing business model transformation in the insurance industry. We conclude that insurtech companies address the emerging customer needs and that traditional incumbent insurers must innovate to keep their prominent role at the customer interface. While novelty and complementarity of on-demand insurance solutions bring value today, we expect that efficiency and customer retention add more value in the future, especially once technology has matured and business model components are well-aligned.