A service composition process typically involves multiple service models. These models may represent the composite and composed services from distinct perspectives, e.g. to model the role of some system that is involved in a service, and at distinct abstraction levels, e.g. to model the goal, interface or orchestration of some service. The consistency among these models needs to be maintained in order to guarantee the correctness of the composition process. Two types of consistency relations are distinguished: interoperability, which concerns the ability of different roles to interoperate, and conformance, which concerns the correct implementation of an abstract model by a more concrete model. This paper gives an overview of the various types of models that may be used in service composition, and explains when interoperability and conformance need to be assessed during the composition process. The paper further focuses on techniques to describe and analyse the interoperability relation using concepts from the COSMO framework. The choice of COSMO allows one to address both interoperability and conformance within a single conceptual framework. For techniques to describe and analyse the conformance relation reference is made to earlier work. Examples are presented to illustrate how different types of models can be used during the service composition process and how interoperability and conformance among these models can be assessed