###### Abstract  
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. Fused Filament Fabrication (FFF); Computational Fluid Dynamics (CFD); Finite Element Analysis (FEA) 1  
[PERSON], [PERSON], M.  
aerospace, biomedical, and automotive engineering has led to an increasing demand for improved print quality, mechanical performance, and dimensional accuracy [3; 4]. Despite its advantages, FFF presents inherent challenges that impact part quality and reliability. Key factors such as thermal fluctuations, residual stresses, interlayer adhesion, and print parameters influence mechanical strength, dimensional stability, and surface finish [5]. These complicated details require numerical simulations, which provide predictive insights into material behavior, enabling the optimization of deposition strategies [6]. Computational models play a crucial role in analyzing melt flow dynamics, cooling and solidification, stress accumulation, and final material properties [7]. Two predominant simulation methods--Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEA)-are widely employed to model the FFF process [8]. CFD is often used to study how polymers flow and transfer heat, while FEA is used to determine the residual stresses, displacement and strain variation, and how well printed parts perform. The integration of these approaches has facilitated the development of more accurate predictive models, contributing to improved process control and part optimization. Beyond traditional thermoplastics, recent advancements in fiber-reinforced composites have expanded the capabilities of FFF [9]. The incorporation of short and continuous fibers into polymer matrices has demonstrated significant improvements in mechanical strength, stiffness, and thermal stability, making FFF a viable solution for high-performance applications [4; 6; 10]. However, fiber integration introduces additional complexities, such as orientation control, dispersion uniformity, and interlayer bonding, requiring advanced numerical modeling techniques to optimize composite performance [7; 8]. In parallel, machine learning has emerged as a promising tool for improving FFF process reliability. Early efforts demonstrated real-time defect detection and interlayer quality prediction using AI-based models [11]. Recent studies have expanded these capabilities by integrating simulation-in-the-loop frameworks [12], thermographic imaging supported by machine learning [13; 14], and closed-loop control systems for adaptive process adjustment in fiber-reinforced printing [15].