The rapid rise of organic-inorganic lead halide perovskites has amazed the photovoltaic community. As the efficiency race continues for this revolutionary class of light-harvesting materials, many questions on the structural, electronic and optical properties of perovskite solar cells have still to be addressed. Computational chemistry as well as computational materials' science and engineering have developed into interdisciplinary and powerful scientific fields. They enclose a portfolio of theories and methods developed in mathematics, physics and chemistry, to help scrutinize and tackle problems that can often not be solved in real experiments. In this dissertation, a compendium of available computational methods that treat matter in the quantum mechanical sense and appropriately link its microscopic behavior with its macroscopic properties are employed. Density Functional Theory (DFT) both in the form of static calculations at zero temperature and in the form of first-principles Molecular Dynamics (MD) simulations have been performed in order to study the structural characteristics, the relative stability and the electronic and optical properties of a variety of lead halide perovskites. Many of the computational studies presented here have been performed in close collaboration with experimental groups. More specifically, in order to tackle the challenge of limited phase stability, the atomistic origins of the preferential stabilization or destabilization of the perovskite phase at room temperature is addressed in the case of mixed cations/mixed halide lead perovskites. Their electronic properties, in turn are investigated in order to examine how mixing affects the properties of the pure compounds. Through these studies, it was possible to formulate new design principles for the synthesis of stable mixed cation/mixed halide perovskites with enhanced optical properties. Furthermore, some fundamental open issues related to the nature of the excited states of lead halide perovskites are addressed by simulating the transient absorption spectra and by studying the possible formation of polarons at room temperature for cesium lead bromide. An understanding of the correlations between the nature of the excited states and the atomistic characteristics of these materials is paving the way for the design of lead halide perovskites with enhanced optical properties. Finally, the anomalous low-temperature behavior of the photoluminescence spectra of cesium lead bromide is rationalized in terms of the structural characteristics of the material at low temperatures. The exploration of such phenomena allowed to gain more insights about the properties of organic-inorganic lead halide perovskites that may make them more suitable for applications within and beyond photovoltaics.