Nanoscale systems are forecast to be a means of integrating desirable attributes of molecular and bulk regimes into easily processed materials. Notable examples include plastic light-emitting devices and organic solar cells, the operation of which hinge on the formation of electronic excited states, excitons, in complex nanostructured materials. The spectroscopy of nanoscale materials reveals details of their collective excited states, characterized by atoms or molecules working together to capture and redistribute excitation. What is special about excitons in nanometre-sized materials? Here we present a cross-disciplinary review of the essential characteristics of excitons in nanoscience. Topics covered include confinement effects, localization versus delocalization, exciton binding energy, exchange interactions and exciton fine structure, exciton-vibration coupling and dynamics of excitons. Important examples are presented in a commentary that overviews the present understanding of excitons in quantum dots, conjugated polymers, carbon nanotubes and photosynthetic light-harvesting antenna complexes.