In natural capital accounting, ecosystems are assets that provide ecosystem services to people. Assets can be measured using both physical and monetary units. In the international System of Environmental-Economic Accounting, ecosystem assets are generally valued on the basis of the net present value of the expected flow of ecosystem services. In this paper we argue that several additional conceptualisations of ecosystem assets are needed to understand ecosystems as assets, in support of ecosystem assessments, ecosystem accounting and ecosystem management. In particular, we define ecosystems’ capacity and capability to supply ecosystem services, as well as the potential supply of ecosystem services.