A fundamental problem associated with the vertical transport of engineered nanomaterials (ENMs) in saturated porous media is the occurrence of nonexponential, for example, nonmonotonic or linearly increasing, retention profiles. To investigate this problem, we compiled an extensive database of ENMs transport experiments in saturated porous media. Using this database we trained a decision tree that shows the order of importance, and range of influence, of the physicochemical factors that control the retention profile shape. Our results help identify domains where current particle-transport models can be used, but also highlight, for the first time, large domains where nonexponential retention profiles dominate and new approaches are needed to understand ENM transport. Importantly, highly advective flow and high ENM influent mass can mask the influence of other physicochemical factors on the retention profile shape; notably, this occurs in 50% of the experiments investigated. Where the relationship between physicochemical factors and retention profile shape can be investigated in detail, our results agree with, and provide validation for, the current understanding of how these factors influence ENM transport.