Folds contain information about the deformation rocks have undergone and the condition of the rocks during deformation. How much of this can we decipher? The geometrical characteristics of folds and the strain distribution within them are perhaps the key to unlocking this information. If the folded layers were originally planar, they reflect inhomogeneous deformation, but without additional originally planar or linear markers of other orientations, we cannot determine the state of strain. The strain in a parallel fold, for example, can be accommodated either by flexural slip or by tangential longitudinal strain, two quite different but geologically realistic strain distributions among an infinite number of possible ones. There are some constraints imposed by fold shapes on possible strain distributions. Fold asymmetry reflects, in most circumstances, sense of shear strain parallel to the general orientation of the folded layering. Problems may arise in shear zones with large strains and in foliated rocks in which kink bands develop at small strains. Information on the orientations of principal stresses cannot be obtained from folds, unless the strain is small and the mechanism of folding understood, as for kink bands, or unless the bulk flow is of constant vorticity, which is difficult to demonstrate. The distribution of measured values of wavelength/thickness in a population of single-layer folds, together with measures of strain and estimates of amplification, can be used to estimate the viscosity ratio of the stiff layer to its matrix and the degree of non-linearity in the flow law, if effective power-law flow is assumed. Information on the rheological state of rocks at the time of folding can also be obtained from the pattern of curvature variation in individual single-layer folds, as demonstrated by the use of computer simulations of folding. Where applied, such methods indicate that the slow natural flow of rock involved in folding is mostly consistent with non-linear power-law rheology, as expected from the results of experimental rock deformation involving crystal-plastic deformation mechanisms.