A total of 23 fungal cellulose-binding domain (CBD) sequences were aligned. Structural models of the cellulosebinding domain of an exoglucanase (CBHII) and of three endoglucanases (EGI, EGII and EGV) from Trichoderma reesei cellulases were homology modelled based on the NMR structure of the fungal cellobiohydrolase CBHI, from the same organism. The completed models and the known structure of the CBHI cellulose-binding domain were refined by molecular dynamics simulations in water. All four models were found to be very similar to the structure of the CBHI cellulose-binding domain and sequence comparison indicated that in general the three-dimensional structures of fungal cellulose-binding domains are very similar. In all the CBDs studied, two disulphide bridges apparently stabilize the polypeptide fold. From the models, an additional disulphide bridge was predicted in EGI and CBHII, and in eight further CBDs from other organisms. Three highly conserved aromatic residues on the hydrophilic side of the wedge make this surface flat This surface is expected to make contact with the substrate. Three invariant amino acids, Gln7, Asn29 and Gln34, on this flat face are in suitable positions for hydrogen bonding with the cellulose surface. Analysis of the differences in the protein surface properties indicated that the endoglucanases tend to be more hydrophilic than the exoglucanases. The largest structural variation was found around positions 12‐16. The fungal CBD sequences are discussed in relation to variations in function and pH dependence. Comparison of the modelled structures with experimental binding data for the CBHI and EGI allowed the formulation of a qualitative relationship to cellulose affinity. This relationship was used to predict the cellulose affinities for 21 CBDs.