  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.
