Enterprise Information Systems (EIS) are increasingly designed with cloud environments in mind, as a set of cooperating services deployed in a mix of platforms, including conventional servers and clouds, private and public. If enterprise value chains are considered, in which their EIS need to cooperate, solving all the interoperability problems raised by the need to meaningfully interconnect all these services constitutes a rather challenging endeavor. This chapter describes the concept of enterprise as a service, a collection of dynamically assembled services with a lifecycle centered on the customers, and proposes a multidimensional interoperability framework to help systematizing the various aspects relevant to interoperability. Besides lifecycle, this framework presents other dimensions, namely concreteness (with various levels of abstraction), interoperability (based on structural compliance and conformance), and concerns (to deal with non-functional aspects such as security, reliability and quality of service).