Using compressive mechanical forces, such as pressure, to induce crystallographic phase transitions and mesostructural changes while modulating material properties in nanoparticles (NPs) is a unique way to discover new phase behaviors, create novel nanostructures, and study emerging properties that are difficult to achieve under conventional conditions. In recent decades, NPs of a plethora of chemical compositions, sizes, shapes, surface ligands, and self-assembled mesostructures have been studied under pressure by in-situ scattering and/or spectroscopy techniques. As a result, the fundamental knowledge of pressure-structure-property relationships has been significantly improved, leading to a better understanding of the design guidelines for nanomaterial synthesis. In the present review, we discuss experimental progress in NP high-pressure research conducted primarily over roughly the past four years on semiconductor NPs, metal and metal oxide NPs, and perovskite NPs. We focus on the pressure-induced behaviors of NPs at both the atomic- and mesoscales, inorganic NP property changes upon compression, and the structural and property transitions of perovskite NPs under pressure. We further discuss in depth progress on molecular modeling, including simulations of ligand behavior, phase-change chalcogenides, layered transition metal dichalcogenides, boron nitride, and inorganic and hybrid organic-inorganic perovskites NPs. These models now provide both mechanistic explanations of experimental observations and predictive guidelines for future experimental design. We conclude with a summary and our insights on future directions for exploration of nanomaterial phase transition, coupling, growth, and nanoelectronic and photonic properties.