Chargeless and extremely light, neutrinos are nevertheless critical to our understanding of particle physics, astrophysics, and cosmology. The first evidence for physics beyond the standard model of particle physics came from neutrino oscillation experiments. Neutrinos allow us to directly probe stellar interiors and play a crucial role in supernova dynamics. Though their masses are small, they affect the large-scale structure of the universe. After a brief introduction to neutrino flavor-mixing and an update on the status of the field, I discuss the near-future directions of flavor-mixing physics and how those directions might impact our understanding of particle physics, astrophysics, and cosmology.