DISAMAR (determining instrument specifications and analysing methods for atmospheric retrieval) is a computer model developed to simulate retrievals of properties of atmospheric trace gases, aerosols, clouds, and the ground surface from passive remote sensing observations in a wavelength range from 270 to 2400 nm. It is being used for the TROPOMI/Sentinel-5P and Sentinel-4/5 missions to derive Level-1b product specifications. DISAMAR uses the doubling–adding method and the layer-based orders of scattering method for radiative transfer calculations. It can perform retrievals using three different approaches: optimal estimation (OE), differential optical absorption spectroscopy (DOAS), and the combination of DOAS and OE, called DISMAS (differential and smooth absorption separated). The derivatives, which are needed in the OE and DISMAS retrievals, are derived in a semi-analytical way from the adding formulae. DISAMAR uses plane-parallel homogeneous atmospheric layers with a pseudo-spherical correction for large solar zenith angles. DISAMAR has various novel features and diverse retrieval possibilities, such as retrieving aerosol layer heights and ozone vertical profiles. This paper provides an overview of the DISAMAR model version 4.1.5 without treating all the details. We focus on the principle of the layer-based orders of scattering method, the calculation of the semi-analytical derivatives, and the DISMAS retrieval method, and it is to our knowledge the first time that these methods are described. We demonstrate some applications of DISMAS and the derivatives.