Background Characterizing the structural properties of protein interaction networks will help illuminate the organizational and functional relationships among elements in biological systems. Results In this paper, we present a systematic exploration of the core/periphery structures in protein interaction networks (PINs). First, the concepts of cores and peripheries in PINs are defined. Then, computational methods are proposed to identify two types of cores, k-plex cores and star cores, from PINs. Application of these methods to a yeast protein interaction network has identified 110 k-plex cores and 109 star cores. We find that the k-plex cores consist of either "party" proteins, "date" proteins, or both. We also reveal that there are two classes of 1-peripheral proteins: "party" peripheries, which are more likely to be part of protein complex, and "connector" peripheries, which are more likely connected to different proteins or protein complexes. Our results also show that, besides connectivity, other variations in structural properties are related to the variation in biological properties. Furthermore, the negative correlation between evolutionary rate and connectivity are shown toysis. Moreover, the core/periphery structures help to reveal the existence of multiple levels of protein expression dynamics. Conclusion Our results show that both the structure and connectivity can be used to characterize topological properties in protein interaction networks, illuminating the functional organization of cellular systems.