Abstract: In crystalline solids, the interaction between the lattice ions and the electrons can give rise to effective quasiparticles whose quantum behavior departs dramatically from that of the free electron. A recently discovered class of materials, known as the Weyl semimetals, hosts charge carriers who act as if they are massless and chiral, thus obeying the Weyl equation that was originally thought to describe the neutrino until the discovery of the neutrino mass in 1998. True to their name, these Weyl quasiparticles exhibit several of the unique effects discovered in the study of the Weyl equation, including the chiral magnetic effect (a charge current produced by application of a magnetic field), and the Adler-Bell-Jackiw anomaly (non-conservation of chiral current). They also give rise to a number of exotic effects in condensed matter physics, including unconventional open Fermi arc surface states and the quantization of a type of topological "charge" that acts like a magnetic monopole in momentum space. In this talk, I will describe how second order nonlinear optical responses can reveal many of these characteristics in surprising ways through our work using laser-driven currents that report on this topological charge and also reveal an unexpected emergent symmetry of the Fermi arc surface states.