<p>Additive manufacturing (AM), particularly metal-based AM, has transformed the manufacturing domain by easing the development of complex, high-performance components with minimal waste. This paper reviews various computational modeling techniques employed in the AM processes, highlighting their trends, advancements, and challenges. It explores fundamental mechanisms such as powder handling, energy-material interactions, melt pool dynamics, microstructural evolution, and defect formation, emphasizing their complexity and the need for accurate models. The paper categorizes computational frameworks into multi-scale and multi-physics models. Micro-scale methods like phase-field modeling, cellular automata, and Monte Carlo techniques, used to predict microstructural changes are discussed in detail. Meso-scale models address intermediate interactions, while macro-scale approaches, such as finite element modeling and CALPHAD-based heat transfer analysis, simulate stress, distortion, and thermal profiles. Emerging data-driven models and real-time simulations, which are pivotal for AM process optimization, are also reviewed in detail. Challenges in aligning computational models with experimental validation due to scalability, cost, and industrial integration barriers are highlighted. Future research areas, including advancements in machine learning, enhanced multi-scale modeling, and improved validation protocols, are discussed in this work.</p>