The article reviews the current status of models that simulate galaxy formation in a cosmological context, focusing on two leading techniques: semi-analytic models and numerical hydrodynamic simulations. The review highlights the evolution of global and structural properties of galaxies from Cosmic High Noon (z ~ 2–3) to the present, noting that while minor discrepancies remain, models show remarkable convergence and qualitative agreement with observations. Key physical processes include cosmological accretion, stellar-driven winds, black hole feedback, and structural evolution through merging and environmental processes. However, many of these processes are modeled phenomenologically, requiring tuning to observations. Emerging multi-scale simulations are helping to bridge the gap between stellar and cosmological scales, and upcoming telescope facilities will provide new constraints on models, particularly through observations of gas inflows and outflows. The article also discusses the observational targets, cosmological background, and the main physical processes involved in galaxy formation, providing an overview of the tools and methods used in both semi-analytic and numerical hydrodynamic simulations.The article reviews the current status of models that simulate galaxy formation in a cosmological context, focusing on two leading techniques: semi-analytic models and numerical hydrodynamic simulations. The review highlights the evolution of global and structural properties of galaxies from Cosmic High Noon (z ~ 2–3) to the present, noting that while minor discrepancies remain, models show remarkable convergence and qualitative agreement with observations. Key physical processes include cosmological accretion, stellar-driven winds, black hole feedback, and structural evolution through merging and environmental processes. However, many of these processes are modeled phenomenologically, requiring tuning to observations. Emerging multi-scale simulations are helping to bridge the gap between stellar and cosmological scales, and upcoming telescope facilities will provide new constraints on models, particularly through observations of gas inflows and outflows. The article also discusses the observational targets, cosmological background, and the main physical processes involved in galaxy formation, providing an overview of the tools and methods used in both semi-analytic and numerical hydrodynamic simulations.