Large-scale protein-protein interaction networks provide new opportunities for understanding cellular organization and functioning. We introduce network schemas to elucidate shared mechanisms within interactomes. Network schemas specify descriptions of proteins and the topology of interactions among them. We develop algorithms for systematically uncovering recurring, over-represented schemas in physical interaction networks. We apply our methods to the S. cerevisiae interactome, focusing on schemas consisting of proteins described via sequence motifs and molecular function annotations and interacting with one another in one of four basic network topologies. We identify hundreds of recurring and over-represented network schemas of various complexity, and demonstrate via graph-theoretic representations how more complex schemas are organized in terms of their lower-order constituents. The uncovered schemas span a wide range of cellular activities, with many signaling and transport related higher-order schemas. We establish the functional importance of the schemas by showing that they correspond to functionally cohesive sets of proteins, are enriched in the frequency with which they have instances in the H. sapiens interactome, and are useful for predicting protein function. Our findings suggest that network schemas are a powerful paradigm for organizing, interrogating, and annotating cellular networks.