Natural proteins have evolved amino acid sequences that provide a native‐structural bias to folding. Structure‐based models (SBMs) of proteins ignore all non‐native interactions and encode this bias by including only interactions present in the native state. SBMs have been remarkably successful at describing the folding mechanisms and folding rates of natural proteins. Non‐native interaction‐enhanced SBMs (eSBMs) of proteins have been developed to understand non‐native traps observed experimentally in several contexts (due to binding sites in the protein, in the crowded environment of the cell, etc.). The mathematical description of the non‐native interactions is problem specific and different in each eSBM. We review the commonly used eSBMs and make a detailed comparison of their non‐native potential energy terms. Designed proteins have not had the benefit of evolution and are more likely to have non‐native intermediates. Experiments have detected the presence of non‐native interactions in the folding kinetics of the designed protein Top7. We compare the intermediate ensembles obtained from folding simulations of Top7 using three different eSBMs and comment on the robustness of these intermediates to changes in the form of non‐native interactions. Although the population of some intermediates is dependent upon the nature of non‐native interactions, the consensus structural information that arises from the different eSBMs is consistent with experiments. Furthermore, the intermediate ensembles indicate the biochemical basis for the experimentally observed non‐native interactions. In summary, eSBMs, as a group, are likely to be a powerful tool for understanding the structural and biochemical basis of non‐native interactions in protein folding.