Neutrino mixing parameters are subject to quantum corrections and hence are scale dependent. This means that the mixing parameters associated to the production and detection of neutrinos need not coincide since these processes are characterized by different energy scales. We show that, in the presence of relatively light new physics, the scale dependence of the mixing parameters can lead to observable consequences in long-baseline neutrino oscillation experiments, such as T2K and NOvA, and in neutrino telescopes like IceCube. We discuss some of the experimental signatures of this scenario, including zero-baseline flavor transitions, new sources of CP-invariance violation, and apparent inconsistencies among measurements of mixing angles at different experiments or oscillation channels. Finally, we present simple, ultraviolet-complete models of neutrino masses which lead to observable running of the neutrino mixing matrix below the weak scale. * There are experimental results that do not fit the three-massive-active-neutrinos paradigm including searches for electron (anti)neutrino appearance at the LSND [5] and experiments as well as the so-called reactor antineutrino anomaly [9,10]. Explanations to these remain elusive and will not be considered in any detail here.