Perovskite materials have emerged as a revolutionary class of semiconductors with significant potential for photovoltaic and optoelectronic applications. Their remarkable optoelectronic properties, including high absorption coefficients, long carrier diffusion lengths, and tunable band gaps, have driven extensive research into their synthesis, stability, and performance. However, challenges related to formation, degradation, and long-term stability of perovskites remain critical for their widespread commercial deployment, as well as toxicity concerns associated with the most widespread lead-halide perovskites. This chapter presents a comprehensive computational investigation into the formation, degradation, and stabilization strategies of both lead-based and lead-free perovskites, with a focus on identifying the key factors that influence their long-term stability. Section 1 introduces the theoretical and computational frameworks employed to study these materials with high accuracy and predictive power. Section 2 explores the mechanisms leading to lead-perovskite formation, highlighting the role of computational approaches in elucidating crystallization pathways and linking theoretical predictions with experimental findings. In particular, ab initio molecular dynamics simulations serve as a precious tool to provide critical insights into the factors that define film morphology and material quality. Finally, the chapter explores the use of chlorinated additives as a strategy for controlling crystal growth. Section 3 shifts focus to degradation mechanisms, particularly those driven by environmental exposure to moisture and oxygen. Here, structural modeling and atomistic simulations of the perovskite/water interface provide insight into decomposition pathways. While the degradation behavior of lead-halide perovskites is examined in detail, particular attention is also given to their tin-based counterparts, which present unique stability challenges. Section 4 discusses a range of passivation strategies designed to enhance the long-term stability of perovskites. Various approaches, including oxysalts, sulfonium-based treatments, mixed-salt passivation, and 2D/3D structural engineering, are evaluated as means to suppress defects, reduce ion migration, and improve device performance. By integrating computational and experimental perspectives, this chapter aims to provide a deeper understanding of how perovskite materials can be optimized for real-world applications. Finally, Sect. 5 provides an overview of lead-free perovskites for photocatalytic applications, with a focus on tin-, germanium-, and bismuth-based systems. These materials are evaluated through a computational lens to assess their structural, electronic, and environmental stability. Through this structured approach, the chapter highlights the synergy between theoretical modeling and experimental validation in addressing the key challenges associated with perovskite materials. The insights presented here contribute to the ongoing efforts to enhance the efficiency, stability, and commercial viability of perovskite-based technologies.