After giving a brief introduction on neutrino oscillations, I discuss two scenarios of non-standard neutrino oscillation physics. First, I consider the loss of quantum coherence in neutrino oscillations, encoded in the size of the neutrino wave packet. It turns out that reactor experiments are especially sensitive to this scenario. I will present the results from our analysis of data from the Daya Bay and RENO experiments, and also show a forecast expected at JUNO. In the second part, I show how neutrino oscillation experiments can be used to test the CPT theorem. This is done by assuming different oscillation parameters for neutrinos and antineutrinos. I discuss this scenario in the context of reactors and the current long baseline experiments NOvA and T2K, and also show a forecast for DUNE.