In contrast with the gas-phase reactions of atmospheric trace gases, there is incomplete or even controversial experimental information on the adsorption and surface state of molecules on ice surfaces due to the difficulties in experimental measurements. The heterogeneous reactions of atmospheric SO2, O3 and H2O2 are of special interest due to their impact on atmospheric pollution and climate. Here, quantum chemical modeling can provide valuable information which is not accessible from the direct measurements and can complement the perceptions obtained by experimental techniques. In the current work, we present the recent results of quantum chemical studies of the structure of adsorption complexes of SO2 molecule on the ice surface and various mechanisms of the further surface reactions of this molecule resulting in the formation of sulfurous acid and ionic dissociation. The comprehensive models of the ice surface, simple and composite models for the quantum chemical treatment of crystalline effects, and the methods suitable for the modeling of the surface reactions are discussed in detail. The results on the original quantum chemical studies of ozone photolysis on the ice surface and the adsorption parameters of possible products of this process (H2O2, HO*, HO-, HOO*, O(1D)) are also discussed. The main goal of these studies was to elucidate the detailed mechanisms of adsorption of two kinds of typical adsorbates (weak acids and non-dissociating species) using the molecular cluster approximation and DFT theory supplemented by the modeling of possible products and intermediates of reactions occurring on the ice surface. Various coordination modes for all these species on the surface or inside the ice Ih crystal were considered: adsorption on the basal and side planes; inclusion into the interstitial space of the ice crystal structure; incorporation into the crystalline network. On this basis, the structures of adsorption complexes, their infrared spectra, and the estimates for the molecular adsorption energies and corresponding thermodynamic parameters were obtained. The comparison between the obtained adsorption energies and the experimental data available from different sources are discussed. In order to describe the kinetic features of adsorption processes at the ice surface, the transition states corresponding to both molecular and ionic pathways of SO2 hydration by water molecules on ice surfaces were located and the corresponding thermodynamic parameters of activation and kinetic rate constants were estimated. Relying on these data, the conclusions about the probability of three different mechanisms of adsorption (molecular hydrolysis to H2SO3, direct addition of OH- to give HSO3-, and relay reaction between remote OH- and adsorbed SO2) are discussed.