As one of the few concepts available to diagnose quantum systems after thermalization, quantum complexity has recently become increasingly important in quantum gravity, e.g., for the black holes information paradox and the interplay of gravity and chaos, as well as in the study of nuclei and exotic matter in low-energy, strong-interaction processes. In this seminar, we will examine a recently proposed entropic measure of quantum complexity, defined in terms of magic (non-stabilizerness), and consider two applications of such a measure: first in the context of lattice gauge theory with direct impact to combinatorial models of quantum geometry, second in the study of the evolution of neutrino flavor states, providing new insight on the neutrino oscillations beyond the use of oscillation probabilities.