Additive manufacturing (AM) is a rapidly growing and evolving form of product development that has the potential to revolutionize both the industrial and academic spheres. For example, AM offers much greater freedom of design while producing significantly less waste than most traditional manufacturing techniques such as injection and blow molding. Filament-based material extrusion AM, commonly referred to as fused filament fabrication (FFF), is one of the most well-known AM modalities using a polymeric feedstock; however, several obstacles currently prohibit widespread use of this manufacturing technique to produce end-use products, which will be discussed in this dissertation. Specifically, a severely limited material catalog restricts tailored product development and the variety of applications. Additionally, poor interlayer adhesion results in anisotropic mechanical properties which can lead to failure, an issue not often observed in traditional manufacturing techniques. A review of the current state of the art research in the field of FFF, focusing on the multiphysics-based modeling of the system and exploring some empirically determined relationships, is presented herein to provide a more thorough understanding of FFF and its complexities. This review further guides the work discussed in this dissertation. The primary focus of this dissertation is to expand the fundamental understanding of the FFF process, which has proven difficult to measure directly. On this size scale, introduction of measurement devices such as thermocouples and pressure transducers can significantly alter the behavior of the process or require major changes to the geometry of the system, leading to spurious measurements, incorrect outcomes, and/or conclusions. Therefore, the research presented in this dissertation focuses on the development and validation of predictive models based on first principles approaches that can provide information leading to the optimization of printing parameters and exploration of novel and/or modified materials without an exhaustive and inefficient trial-and-error process. The first potential issue a novel material may experience in FFF is an inability to extrude from the heated nozzle. Prior to this work, no efforts were focused on the molten material inside the liquefier and its propensity to flow in the reverse direction through the annular region between the filament and the nozzle wall, referred to as annular backflow. The study presented in this dissertation explores this phenomenon, determining its cause and sensitivity to processing parameters and material properties. A dimensionless number, named the "Flow Identification Number" or FIN, is defined that can predict the propensity to backflow based on the material's shear thinning behavior, the filament diameter, the nozzle diameter, and the filament feed rate and subsequent pressure inside the nozzle. An analysis of the FIN suggested that the backflow potential of a given material is most sensitive to the filament diameter and its shear thinning behavior (power law index). The predictive model and FIN were explored using three materials with significantly different onsets of shear thinning. The experiments validated both the backflow model and a previously derived buckling model, leading to the development of a rapid screening technique to efficiently estimate the extrudability of a material in FFF. Following extrusion from the nozzle, the temperature profile of the deposited filament will determine nearly all of the mechanical properties of the printed part as well as the geometry of the individual roads and layers because of its temperature dependent viscoelastic behavior. Therefore, to better understand the influence of the temperature profile on the evolution of the road geometry and subsequent interlayer bonding, a three-dimensional finite element heat transfer analysis was developed. The focus of this study is the high use temperature engineering thermoplastic polymer polyetherimide, specifically Ultem™ 1010, which had not been studied in prior modeling analyses but presents significant challenges in terms of large thermal gradients and challenging AM machine requirements. Through this analysis, it was discovered that convective cooling dominated the heat transfer (on the desktop FFF scale) producing a significant cross-sectional temperature gradient, whereas the gradient along the axis was observed to be significantly smaller. However, these results highlighted a primary limitation in computer modeling based on computational time requirements. This study, utilizing a well-defined three-dimensional model based on a geometry measured empirically, produced results describing 0.5 s of printing time in the printing process and elucidated great details in the road shape and thermal profile, but required more than a week of computation time, suggesting a need for to modify the modeling approach while still accurately capturing the physics of the FFF layer deposition process. The determination of the extensive time required to converge the three-dimensional model, as well as the identification of a relative lack of axial thermal transfer, led to the development of a two-dimensional, cross-sectional heat transfer analysis based on a finite difference approach. This analysis was coupled with a diffusion model and a stress development model to estimate the recovery of the bulk strength and warping potential of a printed part, respectively. Through this analysis, it was determined that a deposited road may remain above Tg for 2-10 s, depending on the layer time, or time required for the nozzle to pass a specific point in the x-y plane between each layer. The predicted strength recovery was significantly overestimated, leading to the discovery of the extreme sensitivity of the predictive models to the relaxation time of a material, particularly at long layer times. When the deposited filament has enough time to attain an equilibrium temperature, small changes in the relaxation time of the material resulted in significant changes in the predicted healing results. These results highlight the need for exact estimations of the material parameters to accurately predict the properties of the final print.