In particle physics there exist two regions: the Standard Model which is fairly complete and the new physics sector which is completely unknown. In between and overlapping with both of these is neutrino physics. In this colloquium I will discuss some algorithmic and theoretical advances to improve our understanding of three-flavor oscillations. I will also discuss how new physics can complicate the oscillation picture. Finally, I will show how astrophysical environments can tell us more about neutrinos and how neutrinos can tell us more about astrophysical environments.