Polaritons, resulting from the hybridization of light with polarization charges formed at the boundaries between media with positive and negative dielectric response functions, can focus light into regions much smaller than its associated free-space wavelength. This property is paramount for a plethora of applications in nanophotonics, ranging from biological sensing to photocatalysis to nonlinear and quantum optics. In the two-dimensional (2D) limit, represented by atomically thin and van der Waals (vdW) materials of single-layers bound by weak vdW attraction, polaritons are characterized by extremely small wavelengths associated with extreme optical confinement, and furthermore can exhibit long lifetimes, electrical tunability, and extreme sensitivity to their dielectric environment, among many other desirable qualities in nano-optical device applications. Here, the fundamentals of polaritons in atomically thin materials are summarized, emphasizing plasmon and exciton polaritons, their strong light–matter interactions, and nonlinear plasmonics. More specifically, this review opens with a pedagogical discussion of plasmons in extended and nanostructured graphene, providing a classical electrodynamical model in a nonretarded theoretical framework, and the ultraconfined acoustic plasmons supported by hybrid graphene–dielectric–metal structures. In addition, the basic principles are introduced and the recent developments on nonlinear graphene plasmonics and on strong coupling physics with atomically thin transition metal dichalcogenides are reviewed. Finally, potentially new, promising research directions in the burgeoning field of 2D nanophotonics are identified.