Quantum mechanics is famously founded on the principle of duality between particles and waves, with far-reaching ramifications in every field of fundamental science – and heavy impact on modern technology. In electronic circuits, one important consequence is that not only the charge and position of the electron, but also its quantum-mechanical phase can be exploited for information transmission and manipulation. As phase control is relatively little explored so far, we develop and synthesize new material platforms where the quantum mechanical “Berry phase” (named after Michael Berry, University of Bristol, UK) strongly affects electronic properties. For example, this is the case in the new generation of ‘topological’ insulators, semimetals, and magnetic materials with linear band dispersion, i.e. with Weyl fermions. By further enriching this materials class with magnetic textures, such as the skyrmion, we ultimately aim for novel optical phenomena and surface states of solids.