Protein structures are key to understanding biomolecular mechanisms and diseases, yet their interpretation is hampered by limited knowledge of their biologically relevant quaternary structure (QS). A critical challenge in inferring QS information from crystallographic data is distinguishing biological interfaces from fortuitous crystal-packing contacts. Here, we tackled this problem by developing strategies for aligning and comparing QS states across both homologs and data repositories. QS conservation across homologs proved remarkably strong at predicting biological relevance and is implemented in two methods, QSalign and anti-QSalign, for annotating homo-oligomers and monomers, respectively. QS conservation across repositories is implemented in QSbio (http://www.QSbio.org), which approaches the accuracy of manual curation and allowed us to predict >100,000 QS states across the Protein Data Bank. Based on this high-quality data set, we analyzed pairs of structurally conserved interfaces, and this analysis revealed a striking plasticity whereby evolutionary distant interfaces maintain similar interaction geometries through widely divergent chemical properties.