to uncover the fundamental properties of these new topological phases of matter. The two most fruitful routes to novel states of matter in modern condensed matter physics have been through “strongly correlated electron materials,” where the strength of the interactions between electrons compares to or exceeds the other energy scales in the system, and through “topological materials,” where the electronic band structure exhibits nontrivial topology. Central to the case of correlated electrons is the Mott insulating phase, in which electron correlations induce an unconventional electrically insulating phase when single-particle band theory would predict metallic conductivity. In the first part of my talk, I will present muon spin relaxation experiments that reveal the first-order nature of the Mott quantum phase transition in two archetypal Mott insulator systems, V2O3 and the rare-earth nickelates RENiO3. I will also show magnetic pair distribution function (mPDF) analysis of neutron scattering experiments on the canonical Mott insulator MnO, shedding light on the short-range magnetic correlations in the paramagnetic state. The mPDF technique is a new method of studying local magnetic structure that I developed as a graduate student. In the final part of my talk, I will focus on some of the very recent breakthroughs in topological materials, including the discovery of emergent Weyl fermions in NbAs and TaAs, and I will discuss how neutrons and photons can be exploited through spin-polarized neutron scattering and angular-resolved photoemission spectroscopy