SCIATRAN is a comprehensive software package for the modeling of radiative transfer processes in the terrestrial atmosphere and ocean in the spectral range from the ultraviolet to the thermal infrared (0.18 - 40 μm) including multiple scattering processes, polarization, thermal emission and ocean-atmosphere coupling. The software is capable of modeling spectral and angular distributions of the intensity or the Stokes vector of the transmitted, scattered, reflected, and emitted radiation assuming either a plane-parallel or a spherical atmosphere. Simulations are done either in the scalar or in the vector mode (i.e. accounting for the polarization) for observations by space-, air-, ship- and balloon-borne, ground-based, and underwater instruments in various viewing geometries (nadir, off-nadir, limb, occultation, zenith-sky, off-axis). All significant radiative transfer processes are accounted for. These are, e.g. the Rayleigh scattering, scattering by aerosol and cloud particles, absorption by gaseous components, and bidirectional reflection by an underlying surface including Fresnel reflection from a flat or roughened ocean surface. The software package contains several radiative transfer solvers including finite difference and discrete-ordinate techniques, an extensive database, and a specific module for solving inverse problems. In contrast to many other radiative transfer codes, SCIATRAN incorporates an efficient approach to calculate the so-called Jacobians, i.e. derivatives of the intensity with respect to various atmospheric and surface parameters.In this paper we discuss numerical methods used in SCIATRAN to solve the scalar and vector radiative transfer equation, describe databases of atmospheric, oceanic, and surface parameters incorporated in SCIATRAN, and demonstrate how to solve some selected radiative transfer problems using the SCIATRAN package. During the last decades, a lot of studies have been published demonstrating that SCIATRAN is a valuable tool for a wide range of remote sensing applications. Here, we present some selected comparisons of SCIATRAN simulations to published benchmark results, independent radiative transfer models, and various measurements from satellite, ground-based, and ship instruments. Methods for solving inverse problems related to remote sensing of the Earth's atmosphere using the SCIATRAN software are outside the scope of this study and will be discussed in a follow-up paper. The SCIATRAN software package along with a detailed User's Guide is freely available for non-commercial use via the webpage of the Institute of Environmental Physics (IUP), University of Bremen: http://www.iup.physik.uni-bremen.de/sciatran.