This thesis introduces new computational methods to better understand key physical phenomena such as light-matter interaction and superconductivity. These processes are governed by the behavior of composite particles: (i) excitons, which explain how materials absorb and emit light, and (ii) Cooper pairs, the building blocks of superconductivity. Using quantum mechanics and first-principles simulations, based entirely on fundamental physical laws, this research enables the study of such composite particles at the atomic scale, and it facilitates the interpretation of experimental results. Theoretical models were extended and new software tools developed to predict how excitons and Cooper pairs behave in realistic environments. The thesis explores several material systems, ranging from two-dimensional semiconductors to layered superconductors. These studies reveal how external conditions such as electric fields, lattice strain, or temperature influence the structure and dynamics of the composite particles involved. The insights gained here are crucial for the design of future technologies, including quantum computers, light-based electronics, and next-generation superconductors. By deepening our fundamental understanding of matter at the quantum level, this work helps bridge the gap between theoretical physics and technological innovation.