After a brief review of dynamic correlations in equilibrium fluids, we consider the long-range correlations between the fluctuations in a fluid subjected to a large stationary temperature gradient. These long-range correlations enhance and modify the Rayleigh spectrum of the fluid. We elucidate that the modifications of the Rayleigh line are determined by the coupling of the entropy fluctuations to the transverse velocity fluctuations. Recent attempts to test the theoretical predictions with the aid of light-scattering experiments are discussed