MOTIVATION: Most protein-structure superimposition tools consider only Cartesian coordinates. Yet, much of biology happens on the surface of proteins, which is why proteins with shared ancestry and similar function often have comparable surface shapes. Superposition of proteins based on surface shape can enable comparison of highly divergent proteins, identify convergent evolution and enable detailed comparison of surface features and binding sites. RESULTS: We present ZEAL, an interactive tool to superpose global and local protein structures based on their shape resemblance using 3D (Zernike-Canterakis) functions to represent the molecular surface. In a benchmark study of structures with the same fold, we show that ZEAL outperforms two other methods for shape-based superposition. In addition, alignments from ZEAL were of comparable quality to the coordinate-based superpositions provided by TM-align. For comparisons of proteins with limited sequence and backbone-fold similarity, where coordinate-based methods typically fail, ZEAL can often find alignments with substantial surface-shape correspondence. In combination with shape-based matching, ZEAL can be used as a general tool to study relationships between shape and protein function. We identify several categories of protein functions where global shape similarity is significantly more likely than expected by random chance, when comparing proteins with little similarity on the fold level. In particular, we find that global surface shape similarity is particular common among DNA binding proteins. AVAILABILITY AND IMPLEMENTATION: ZEAL can be used online at https://andrelab.org/zeal or as a standalone program with command line or graphical user interface. Source files and installers are available at https://github.com/Andre-lab/ZEAL. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.