Methods for calculation of kinetic isotope effects and their application to reactions catalysed by enzymes are surveyed, including consideration of cut-off approximations both old and new, empirical bond-order–bond-energy approaches, quantum-mechanical cluster methods, and hybrid quantum mechanics/molecular mechanical methods. The unifying feature is the use of a Hessian matrix of force constants within the harmonic approximation. The merits of methods appropriate for supramolecular systems, including enzymes, are discussed in contrast to commonly used methods developed for gas-phase molecules, and the importance of averaging in conformationally flexible systems is emphasised.