In this talk, I will discuss rich topological behavior in two related models – the Majorana wire and a Su-Schrieffer-Heeger ladder- in the presence of potential energy landscapes. An introduction of the two models and of techniques that directly provide information on edge-state properties will form the starting point for obtaining topological phase diagrams in these models. In the case of these systems subject to a quasiperiodic potential, a beautiful topological phase diagram emerges mimicking Hofstadter’s butterfly patterns. In the case of disordered potential landscapes, Anderson localization physics informs the behavior of the disordered topological phase diagram.  Finally, I will discuss the possible implementation of this physics in a variety of experimental systems, including solid state, cold atomic and electro-mechanical settings.