A comprehensive investigation of the luminescent properties of carbon nitride polymers, based on tri-s-triazine units, has been conducted. Steady-state temperature- and excitation-power-dependent as well as time-resolved measurements with near-UV excitation (λ=325 nm and 405 nm) yield strong photoluminescence, covering the visible spectrum. The spectral, thermal, and temporal features of the photoluminescence can be satisfactorily described by the excitation and radiative recombination of molecular excitons, localized at single tri-s-triazine units. The discussed model is in accordance with the recently reported absorption features of carbon nitride polymers. Thus, from the point of view of optical spectroscopy, the material effectively behaves as a monomer.