Physical models of galaxy formation in a cosmological framework are essential for understanding how galaxies evolve over time. These models use two main techniques: semi-analytic models and numerical hydrodynamic simulations. They focus on the evolution of galaxies from Cosmic High Noon (z ~ 2-3) to the present, aiming to predict observed properties such as stellar mass, star formation rates, and galaxy morphology. Despite some discrepancies, models show convergence and qualitative agreement with observations. Key processes include cosmological accretion, stellar-driven winds, black hole feedback, and structural evolution through mergers and environmental factors. However, many processes are modeled phenomenologically, requiring tuning to observations. Emerging simulations bridge scales, improving model accuracy. Upcoming telescopes will provide new constraints, particularly on gas inflows and outflows. Observational targets include global properties, scaling relations, and structural features. Models have advanced significantly, with numerical simulations and semi-analytic models providing insights into galaxy formation. These models now serve as essential tools for understanding galaxy evolution, with ongoing research aiming to refine predictions and improve physical accuracy.Physical models of galaxy formation in a cosmological framework are essential for understanding how galaxies evolve over time. These models use two main techniques: semi-analytic models and numerical hydrodynamic simulations. They focus on the evolution of galaxies from Cosmic High Noon (z ~ 2-3) to the present, aiming to predict observed properties such as stellar mass, star formation rates, and galaxy morphology. Despite some discrepancies, models show convergence and qualitative agreement with observations. Key processes include cosmological accretion, stellar-driven winds, black hole feedback, and structural evolution through mergers and environmental factors. However, many processes are modeled phenomenologically, requiring tuning to observations. Emerging simulations bridge scales, improving model accuracy. Upcoming telescopes will provide new constraints, particularly on gas inflows and outflows. Observational targets include global properties, scaling relations, and structural features. Models have advanced significantly, with numerical simulations and semi-analytic models providing insights into galaxy formation. These models now serve as essential tools for understanding galaxy evolution, with ongoing research aiming to refine predictions and improve physical accuracy.