In this paper, we investigate the notion of partnership as found in security models for key exchange protocols. Several different approaches have been pursued to define partnership, with varying degrees of success. We aim to provide an overview and criticism of the various definitions and point out some pitfalls that can be encountered when trying to define partnership. As a result, we propose an intuitive way of defining partnership directly from equality of session keys. In addition, we show that authentication can be captured using a definition of partnership by equality of partner identifiers, and give proofs that both definitions achieve what we expect from them.