Fused Filament Fabrication (FFF) has become a widely adopted additive manufacturing technology due to its cost-effectiveness, material versatility, and accessibility. However, optimizing process parameters, predicting material behavior, and ensuring structural reliability remain major challenges. This review analyzes state-of-the-art computational methods used in FFF, which are categorized into four main areas: melt flow dynamics, cooling and solidification, thermal–mechanical behavior, and material property characterization. Notably, the integration of Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEA) has led to improved predictions of key phenomena, such as filament deformation, residual stresses, and temperature gradients. The growing use of fiber-reinforced filaments has further enhanced mechanical performance; however, this also introduces added complexity due to filler orientation effects and interlayer adhesion issues. A critical limitation across existing studies is the lack of standardized experimental validation methods, which hinders model comparability and reproducibility. This review highlights the need for unified testing protocols, more accurate multi-physics simulations, and the integration of AI-based process monitoring to bridge the gap between numerical predictions and real-world performance. Addressing these gaps will be essential to advancing FFF as a precise and scalable manufacturing platform.