In two-dimensional materials like bilayer graphene, stacking faults appear as lines that thread through the sample. Any electron traversing the material has to cross such lines, which provide quantum mechanical barriers. Due to the specific Bernal stacking in bilayer graphene and its two-fold degeneracy, the case is a non-trivial quantum-mechanical problem. We have strong indicators that many phenomena, which have been observed in bilayer graphene (and that have been tentatively explained by many-body effects), can be traced back to the unavoidable presence of stacking faults. Graphene bilayer, however, provides a particularly clear example on how important stacking faults in the low-dimensional materials are, because one can fully read out its open-lying defect structure. We will use this opportunity to obtain as much as structural information as possible (by TEM, STM, AFM, etc.), that are combined with electronic data (transport, magneto-transport, Leem potentiometry mapping), optical imaging (plasmon mapping), and specially adapted quantum-mechanical calculations in order to develop a full picture of the underlying physics. We will explore techniques to manipulate stacking faults, either mechanically, thermally, or current-driven. The unprecedented approach will yield results that are valuable for any stacked two-dimensional material.