With the number of known protein folds potentially approaching completion, the problems associated with their systematic classification are evaluated. It is argued that it will be difficult, if not impossible, to find a general metric based on pairwise comparison that will provide a satisfactory classification. It is suggested that some progress may be made through comparison against a library of idealised ‘template’ folds, but a proper solution can only be attained if this includes a model of the underlying evolutionary processes. These processes are considered with examples of some unexpected relationships among folds, including circular permutations. The problem is finally set in the wider context of the genetic environment, introducing complications relating to introns, gene fixation and population size.