This work describes the development of the new discrete ordinate scattering algorithm, which is a part of the Atmospheric Radiative Transfer Simulator (ARTS). Furthermore, applications of the algorithm, which was implemented to study for example the influence of cirrus clouds on microwave limb sounding, are presented. The model development requires as a theoretical basis the electromagnetic scattering theory. The basic quantities are defined and different methods to compute single scattering properties of small particles are discussed. The phenomenological derivation of the vector radiative transfer equation, which is the basic equation of the model, is outlined. In order to represent clouds as scattering media in radiative transfer models, information about their micro-physical state is required as an input for calculating the scattering properties. The micro-physical state of a cloud is defined by the phase of the cloud particles, the particle size and shape distributions, the particle orientation, the ice mass or the liquid water content, and the temperature. The model uses the Discrete Ordinate ITerative (DOIT) method to solve the vector radiative transfer equation. The implementation of a discrete ordinate method is challenging due to the spherical geometry of the model atmosphere, which is required for the simulation of limb radiances. The involved numerical issues, grid optimization and interpolation methods, are discussed. The new scattering algorithm was compared to three other models, which were developed during the same time period as the DOIT algorithm. Overall, the agreement between the models was very good, giving confidence in new models. Scattering simulations are presented for limb- and down-looking geometries, for one-dimensional and three-dimensional spherical atmospheres. They were performed for the frequency bands of the Millimeter Wave Acquisitions for Stratosphere/Troposphere Exchange Research (MASTER) instrument, and for selected frequencies of the Earth Observing System Microwave Limb Sounder (EOS MLS). The simulations show the impact of cloud particle size, shape and orientation on the brightness temperatures and on the polarization of microwave radiation in the atmosphere. The cloud effect is much larger for limb radiances than for nadir radiances. Particle size is a very important parameter in all of the simulations. The polarization signal is small for simulations with randomly oriented particles whereas for horizontally aligned particles with random azimuthal orientation the polarization signal is significant. Moreover, the effect of particle shape is only relevant for oriented cloud particles. The simulations show that it is essential to use a three-dimensional scattering model for inhomogeneous cloud layers.