This chapter presents an in-depth description of the theory of scattered-light DOAS measurements for various observation geometries in the troposphereTroposphere and stratosphereStratosphere. This includes approaches for the determination of Air Mass Factors (AMF) and a review of current radiation transport models used for these calculations. The chapter introduces the concepts of altitude sensitivity and Box Air Mass FactorsBox Air Mass Factor (BAMF) (BAMFs) and their use in vertical concentrationConcentration profiles retrievals from multi-axis DOASMulti-Axis DOAS (MAX-DOAS) measurements using the optimal estimation technique. This is followed by a discussion on the challenges of vertical column densityVertical Column Density (VCD) and profile retrievals from satellite observations. Further topics include the use of Fraunhofer reference spectra for the determination of absolute trace gas slant column densities and the treatment of the Raman scatteringRaman scattering in the atmosphere (Ring Effect)Ring effect.