Fluorescence correlation spectroscopy (FCS) determines rates of molecular transport and chemical reactions from measurements of spontaneous concentration fluctuations in small open sub-volumes of systems in equilibrium or non-equilibrium steady state. The concentration fluctuations are monitored via fluorescence. Although difficult at first, FCS measurements are now in routine use in areas of chemistry, physics and biology. The initial approach has given rise to a wide range of extensions and variations that yield information about the dynamics of molecular processes in simple systems and living cells. FCS provides a window on a mesoscopic world in which molecular fluctuations are both detectable and (for biological cells) possibly functionally important. Moreover, FCS is a precursor to single molecule measurements.