Scattering from X-ray Mirrors deals with the the phenomena observed when x-rays are reflected from high quality mirror surfaces at grazing incidence. The presence of micro- irregularities in the reflecting surface causes power to be deviated away from the specular direction and into the wings of the angular distribution of radiation. Both theoretical and experimental investigations are presented. The two principal theories of the scattering of electromagnetic radiation are reviewed and are shown to produce identical results in the smooth surface limit. The scalar theory is further developed so as to be applicable to a scattering surface which can be described by an arbitrary surface height distribution function for any surface autocovariance function. The theoretical advances reported suggest a means by which the surface height distribution statistics of mirror surfaces might be derived from experimental scattering measurements. The experimental work in the thesis deals with a scattering experiment designed to test these theoretical developments. The development work involved in the construction of the Variable Angle Scattering Experiment (VASE) is presented and the anomalous results obtained from scattering measurements from two test flat x-ray mirrors are discussed. A shadowing model is devised to account for the anomalous results from the VASE. The shadowing model is then shown to be in good agreement with the VASE data and with data from other scattering experiments. The shadowing model, which provides a means of measuring the properties of pure mirror surfaces, is further developed to enable measurements of surface structure on mirrors which have become specked with small sparse contaminant features, thus allowing highly sensitive estimates of contaminant density and height to be made.