Papers in algebraic number theory these days often include a lot of cohomological language, with Galois cohomology being one of the recurring flavors. In this talk, I will explain how to think about Galois cohomology in an elementary manner, and why it occupies a foundational place in class field theory. I include an application to the Scholz reflection principle (which states that the quadratic fields of discriminant D and -3D have almost the same amount of 3-torsion in their class groups).