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Molecules are found in diverse astronomical conditions, ranging from star-forming regions to the outer envelopes of carbon stars and from objects in our solar system to distant metal-poor galaxies. The complexity of these molecules ranges from simple diatomic molecules to amino acids such as glycine. Their association with various phases of star and planet formation are of particular interest; they can serve as building blocks of more complex molecules and provide an insight into the primordial composition of our planet Earth, thereby addressing the question of how life originated on Earth. In addition, molecules serve as valuable probes of the physical conditions of their environments and are closely linked to the lifetimes of their sources. Many species not observed under terrestrial conditions are of special importance for what they reveal about the build-up of molecular complexity across the Universe. To address the question of how these molecules form requires a physics-driven, multi-scale approach: from quantum-chemical processes on icy dust grains, to kinetic networks in protoplanetary disks, and ultimately to the macroscopic dynamics of star-forming regions and planetary atmospheres. Numerical simulations are central in connecting these scales, allowing us to trace the evolution from simple precursors into complex organic species under varying physical properties such as density, temperature, and radiation conditions. In this talk, I will discuss how numerical simulations can be used to study molecular formation across diverse astrophysical environments, emphasising star-forming regions, comets, and exoplanets. |