Enzyme catalysis is governed by a limited toolkit of residues and organic or inorganic co-factors. Therefore, it is expected that recurring residue arrangements will be found across the enzyme space, which perform a defined catalytic function, are structurally similar and occur in unrelated enzymes. Leveraging the integrated information in the Mechanism and Catalytic Site Atlas (M-CSA) (enzyme structure, sequence, catalytic residue annotations, catalysed reaction, detailed mechanism description), 3D templates were derived to represent compact groups of catalytic residues. A fuzzy template-template search, allowed us to identify those recurring motifs, which are conserved or convergent, that we define as the "modules of enzyme catalysis". We show that a large fraction of these modules facilitate binding of metal ions, co-factors and substrates, and are frequently the result of convergent evolution. A smaller number of convergent modules perform a well-defined catalytic role, such as the variants of the catalytic triad (i.e. Ser-His-Asp/Cys-His-Asp) and the saccharide-cleaving Asp/Glu triad. It is also shown that enzymes whose functions have diverged during evolution preserve regions of their active site unaltered, as shown by modules performing similar or identical steps of the catalytic mechanism. We have compiled a comprehensive library of catalytic modules, that characterise a broad spectrum of enzymes. These modules can be used as templates in enzyme design and for better understanding catalysis in 3D.