Understanding data from hadron colliders such as RHIC and the LHC requires understanding the structure of the colliding hadrons. At the same time, studying the structure of nucleons allows us to probe the strong interactions of confined quarks and gluons. The momentum distributions of quarks and gluons in nucleons are encoded in parton distribution functions (PDFs). Extracting PDFs from experimental data relies on several assumptions, and finding where these assumptions break down can reveal new insights about QCD in poorly understood regimes. In this talk, I will present measurements by the LHCb collaboration that challenge some of these assumptions by probing the structure of nucleons in extreme conditions. I will present a study of Z-boson production in association with charm quarks that could point to a non-perturbative contribution to the charm quark PDF. I will also present studies of particle production in proton-lead collisions and discuss their implications for nuclear modifications of PDFs and QCD at high gluon densities.