Perovskite-based solar cells are currently the most rapidly advancing photovoltaic technology but concerns about their long-term stability are still impeding full-scale commercialization. This thesis provides computational insights into some of the stability-related issues in perovskite-based photovoltaic devices. In a first part of the thesis, the effect of different additives on the stability and performance of perovskite photovoltaic materials are investigated in collaboration with experimental groups. The work provides detailed insights into the molecular interaction mechanisms of different additives with perovskite surfaces. Generally, it is found that the size match of the additive with respect to the perovskite lattice binding sites is crucial for maximizing the passivation effect. Specifically, the computational studies presented here on two different bifunctional additives show that while both molecules bind strongly to the Pb site via electron-donor functional groups, the 2,5-thiophenedicarboxylic acid molecule is less compatible with the lattice than biphenyl-4,4'-dithiol. Furthermore, due to its larger effective surface coverage, the latter is more suitable to protect the surface from moisture and from FA+ and I- loss, thereby reducing the formation of defects. The small monofunctional anionic additive triiodide I3- on the other hand, exhibits no surface shielding effect. Instead, this additive binds strongly to halide vacancy defects, thereby suppressing nonradiative recombination and increasing charge carrier mobility. In addition, due to its suitable redox properties, it can simultaneously oxidize metallic Pb0 defects under production of two I- ions that can passivate further halide vacancies. At contrast, addition of medium-sized organic cations can induce the formation of lower dimensional (quasi) 2D structures. The latter are explored here in more detail by considering both iodide and bromide variants of Dion-Jacobson and Ruddlesden-Popper 2D perovskites based on 1,4-phenylenedimethylammonium (PDMA) and benzylammonium (BzA) spacers with special view on their pressure-induced mechanochromic properties in the 0-0.35 GPa pressure range, which is relevant for practical applications. Here, density functional theory (DFT) calculations provide insights into the structural changes within the organic spacer layer and the organic-inorganic interface. The most significant shift in the optical absorption is observed in (BzA)2PbBr4 under 0.35 GPa pressure, which is attributed to an isostructural phase transition. Finally, in order to study and understand such and similar phase transitions in perovskite systems on a fundamental level, accurate force fields (FF) that properly capture the relative phase stability as a function of temperature are of essence. To that end, in the second part of this thesis, an in-house version of a force matching code especially designed for the all-inorganic CsPbI3 (for which previous results for both a nonpolarizable as well as a polarizable model are presented) has been extended to be applicable to arbitrary systems, which implied a generalization to take intermolecular as well as intramolecular polarization effects into account and include atomic multipoles up to quadrupoles. The new implementation has been applied to the hybrid organic-inorganic halide perovskite FAPbI3, for which a fixed-point charge FF has been generated via force matching.