Nanoparticles are commonly used in various fields of applications such as electronics, catalysis or engineering where they can be subjected to a certain amount of stress leading to structural instabilities or irreversible damages. In contrast with bulk materials, nanoparticles can sustain extremely high stresses (in the GPa range) with ductility, even in the case of originally brittle materials. This review article focuses on the modeling of the mechanical properties of nanoparticles, with an emphasis on elementary deformation processes. Various simulation methods are described, from classical molecular dynamics calculations, the best suited method when applied to the modeling the mechanics of nanoparticles, to dislocation dynamics based hybrid methodologies. We detail the mechanical behaviour of nanoparticles for a large array of material classes (metals, semiconductors , ceramics, etc.), as well as their deformation processes. Regular crystalline nanoparticles are addressed, as well as more complex systems such as nanoporous or core-shell particles. In addition to the exhaustive review on the recent works published on the topic, challenges and future trends are proposed, providing solid foundations for forthcoming investigations.