Over the last decades, cosmological simulations of galaxy formation have been instrumental for advancing our understanding of structure and galaxy formation in the Universe. These simulations follow the non-linear evolution of galaxies modeling a variety of physical processes over an enormous range of scales. A better understanding of the physics relevant for shaping galaxies, improved numerical methods, and increased computing power have led to simulations that can reproduce a large number of observed galaxy properties. Modern simulations model dark matter, dark energy, and ordinary matter in an expanding space-time starting from well-defined initial conditions. The modeling of ordinary matter is most challenging due to the large array of physical processes affecting this matter component. Cosmological simulations have also proven useful to study alternative cosmological models and their impact on the galaxy population. This review presents a concise overview of the methodology of cosmological simulations of galaxy formation and their different applications.
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