Many years of research effort, after the synthesis of graphene, have revealed that atomically thin two-dimensional materials have mechanical, electronic, and optical properties which are different from their bulk counterparts. Thus, the interest in twodimensional materials is growing which is also fueled by fast advances in synthesis and measurement techniques. In this regard, the theoretical and computational simulations provide physical insight to the experiments in this new and demanded field; a tool for characterizing these materials; and also a reliable prediction approach to possible stable structures. The density functional theory (DFT) is one of the most powerful and commonly used methods for such theoretical investigations. The DFT-based computational determination of optical properties, as compared to other usual DFT-based calculations, is in its early stage due to high computational resource requirements and lack of established documentation. Therefore, the present thesis aims at giving the methodology and computing the optical properties of ultra-thin materials by using DFT and beyond-DFT approaches. More precisely, the thesis provides an overview of light matter interaction; basics of DFT, GW approximation for many-body effects, Bethe-Salpeter equation for excitonic effects; and several applications of these on atomically-thin systems.