"Understand, predict, and design" has been for a long time the informal mission statement of our group; since occasionally we do follow through on this, I'll take the chance to illustrate the paradigm with case studies taken from the burgeoning field of 2D materials. I'll discuss in particular the breakdown of the established but approximate picture of phonons being the heat carriers in crystals, the engineering of Berry phases in nanostructures to create 1D electron and hole wires, and our ongoing efforts to exfoliate all known 3D materials.