Understanding the formation and evolution of galaxies is a fundamental challenge in astrophysics, necessitating a comprehensive comparison between theoretical models and observational data. This paper reviews the critical role of numerical simulations in modeling the complex physical processes that govern galaxy formation over cosmic time. By employing advanced computational techniques, researchers can simulate the gravitational interactions of dark matter, the dynamics of baryonic matter, and the intricate feedback mechanisms that influence star formation and galaxy morphology. The theoretical foundations of galaxy formation are grounded in the Λ Cold Dark Matter (ΛCDM) cosmology, which provides a framework for understanding the initial conditions of the universe. The paper discusses the significance of initial density fluctuations, as described by the primordial power spectrum, and their evolution under gravitational collapse, leading to the formation of dark matter halos. The Press-Schechter formalism and its extensions are highlighted as essential tools for predicting halo abundance and mass distribution. In addition to dark matter dynamics, the paper delves into baryonic physics, emphasizing processes such as gas cooling, star formation, and chemical enrichment. The interplay between these processes is crucial for reproducing observed galaxy properties, and the paper outlines various hydrodynamical techniques employed in simulations, including Smoothed Particle Hydrodynamics (SPH) and Adaptive Mesh Refinement (AMR).Key simulation projects, such as the Millennium Simulation, EAGLE, Illustris, and FIRE, are systematically compared, showcasing their unique strengths and contributions to the field. The results of these simulations are juxtaposed with observational data from large surveys like the Sloan Digital Sky Survey (SDSS) and the Galaxy and Mass Assembly (GAMA) survey. The paper presents a detailed analysis of the galaxy stellar mass function, size-mass relation, and star formation main sequence, illustrating both the successes and the ongoing challenges in accurately modeling galaxy properties. Ultimately, this review underscores the importance of continued refinement in simulation methodologies and the integration of observational insights to enhance our understanding of galaxy formation and evolution. By addressing existing discrepancies and exploring future research directions, this work aims to contribute to the broader discourse on the nature of galaxies and their role in the universe.