When a protein folds or unfolds, it passes through many half-folded microstates. Only a few of them can accumulate and be seen experimentally, and this happens only when the folding (or unfolding) occurs far from the point of thermodynamic equilibrium between the native and denatured states. The universal features of folding, though, are observed just close to the equilibrium point. Here the 'two-state' transition proceeds without any accumulation of metastable intermediates, and only the transition state ('folding nucleus') is outlined by its key influence on the folding-unfolding kinetics. Our aim is to review recent experimental and theoretical studies of the folding nuclei.