Many sites with high solar radiation face high dust loads that reduce energy generation by concentrated solar power plants. This review presents the attenuative impacts of atmospheric aerosols, as well as reflectivity losses due to soiling of solar reflectors, by covering both experimental investigations and numerical studies; along with presenting the theoretical background. The chemical nature of aerosols, and the physics of soiling and atmospheric extinction phenomena (scattering and absorption) are also reviewed. Suspended particles like aerosols result in atmospheric extinction of the solar radiation that reaches the concentrators, and the deposition of these particles on the solar reflectors provokes decreases up to 80% in their reflectivity, and thus enhances the cumulus of optical losses and the reduction of energy production. Even though dust affects both CSP and photovoltaics, CSP technologies suffer more losses. The impact of dust should be particularly considered during the planning phase of solar thermal plants, since its consequent reduction in energy output can be severe. While there have been multiple papers to review dust-related problems for PV, the present paper is the first literature review dedicated to the impact of soiling on concentrated solar power.