Fault-propagation folds are common structures that accommodate crustal shortening in various compressional settings worldwide. Motivated by the wide range of geometries observed for fault-propagation folds, we investigated the role played by mechanics in the variations observed for this structural class. Detailed structural measurements of a series of 15 fault-propagation folds from the Niger Delta, Argentina, and southeastern Asia reveal several relationships between aspects of the structural geometries. We found that the decrease in displacement updip along the fault is well approximated by a linear trend that has a relatively consistent slope, and that this gradient remains constant for increasing total displacement. This suggests that the faults propagate self-similarly, consistent with a range of kinematic models that have been used to describe them. Additionally, we observed that uplift has contributions both from rigid translation along a dipping fault and folding, and that the values observed for many natural structures lie between those predicted by the trishear and kink-style models, such as fixed-axis and constant-thickness fault-propagation folding. Finally, we found that fault-propagation folds exhibit a range of fault dips, with many structures having fault dips coincident with those characteristic of fault-bend folds, while another group is characterized by significantly higher fault dips. By developing a series of discrete-element mechanical models, we found that mechanical layering plays a first-order role in the development of different styles of fault-propagation folding. Homogeneous materials produce trishear-like fault-propagation folds, while strongly layered materials produce structures more similar to the kink-style kinematic models. Comparison with the observations from natural structures indicates that these mechanical models reproduce the observed trends, and that most natural structures fall between these two styles of models. This suggests that trishear and the kink-style (fixed-axis and constant-thickness) fault-propagation folding models may be thought of as end members on a continuum of possible fault-propagation folding geometries that are largely dictated by the degree of mechanical layer anisotropy in the stratigraphy. Finally, we suggest that fault steepening in highly anisotropic models may develop due to strain localization in tightly folded structural forelimbs.