Only about 1000 qualitatively different protein folds are believed to exist in nature. Here, we review theoretical studies which suggest that some folds are intrinsically more designable than others, i.e. are lowest energy states of an unusually large number of sequences. The sequences associated with these folds are also found to be unusually thermally stable. The connection between highly designable structures and highly stable sequences is generally known as the 'designability principle'. The designability principle may help explain the small number of natural folds, and may also guide the design of new folds. (C) 2003 Elsevier Ltd. All rights reserved.