Fluorescence correlation spectroscopy (FCS) is a single molecule technique used mainly for determination of mobility and local concentration of molecules. This review describes the specific problems of FCS in planar systems and reviews the state of the art experimental approaches such as 2-focus, Z-scan or scanning FCS, which overcome most of the artefacts and limitations of standard FCS. We focus on diffusion measurements of lipids and proteins in planar lipid membranes and review the contributions of FCS to elucidating membrane dynamics and the factors influencing it, such as membrane composition, ionic strength, presence of membrane proteins or frictional coupling with solid support.