Time-resolved fluorescence spectroscopy of molecular aggregates is described using the response function theory, which incorporates exciton dynamics through nonequilibrium Green's functions. The dynamics are simulated using nonperturbative density matrix theory, which allows us to describe spectral and temporal signatures of various system-bath coupling regimes. We find that the conventional excitonic picture of eigenstates is valid in the Markovian regime. In the non-Markovian regime, the exciton concept breaks down and renormalized quantities can be introduced. Effective intermolecular coupling, widely used in polaron theories, can be used to account for the effects of the bath.