Weakly interacting quasiparticles play a central role in the low-energy description of many phases of quantum matter. At higher energies, however, quasiparticles cease to be well defined in generic many-body systems owing to a proliferation of decay channels. In this review, we discuss the phenomenon of quantum many-body scars, which can give rise to certain species of stable quasiparticles throughout the energy spectrum. This goes along with a set of unusual nonequilibrium phenomena including many-body revivals and nonthermal stationary states. We provide a pedagogical exposition of this physics via a simple yet comprehensive example, that of a spin-1 XY model. We place our discussion in the broader context of symmetry-based constructions of many-body scar states, projector embeddings, and Hilbert space fragmentation. We conclude with a summary of experimental progress and theoretical puzzles.