Structural insights into protein complexes have had a broad impact on our understanding of biological function and evolution. In this work, we sought a comprehensive understanding of the general principles underlying quaternary structure organization in protein complexes. We first examined the fundamental steps by which protein complexes can assemble, using experimental and structure-based characterization of assembly pathways. Most assembly transitions can be classified into three basic types, which can then be used to exhaustively enumerate a large set of possible quaternary structure topologies. These topologies, which include the vast majority of observed protein complex structures, enable a natural organization of protein complexes into a periodic table. On the basis of this table, we can accurately predict the expected frequencies of quaternary structure topologies, including those not yet observed. These results have important implications for quaternary structure prediction, modeling, and engineering.