Abstract The structure of cellulose fibre is discussed in relation to the relevance of the ligand–receptor concept for dye–fibre binding. An outline of qualitative SAR (structure–activity relationship) for dye–cellulose fibre binding is given, as well as of QSAR/QSPR (quantitative structure–activity/property relationship) for such binding and calculations of pertinent (electronic, geometric and partition) properties of dye molecules. Modern QSAR methods for dye–fibre adsorption include MTD (minimal steric difference) analysis, CoMFA (comparative molecular field analysis), PCRA (principal component regression analysis) and neural network. Series of anthraquinone vat dyes, mono, bisazo and disperse dyes were studied by these methods. Conclusions from these QSAR studies concerning the effect of structural features of dye molecules upon adsorption on cellulose fibres are discussed.