In the past decade, neutrino experiments have emerged as powerful tools in the search for new physics beyond just oscillations. In these fixed-target experiments, new particles (e.g. dark photons, millicharged particles, light scalars, etc.) can be produced in the neutrino beamline and propagate into the downstream detector where they induce signals via scattering or decay. These experiments are capable of probing models of light (MeV-scale) dark matter and can be considered complementary to more traditional direct and indirect searches. In the first half of this talk, I will describe the sensitivity of existing LSND measurements and future data from the JSNS2 experiment to two dark matter models. In particular, I will show that JSNS2 can rule out new parameter space for dark photon models and that LSND severely constrains a recent explanation of the 3.5 keV Galactic Center excess. For the second half of the talk, I will discuss the recently updated MiniBooNE neutrino oscillation analysis and possible new physics explanations for the long-standing low energy excess. Through model-independent, kinematic arguments, I will show that many new physics explanations for the excess are incompatible with the available data.