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. / Doctor of Philosophy / Additive manufacturing (AM), particularly filament-based material extrusion additive manufacturing, commonly known as fused filament fabrication (FFF), has recently become the subject of much study with the goal of utilizing it to produce parts tailored to specific purposes quickly and cheaply. AM is especially suited to this purpose due to its ability to produce highly complex parts with the ability to change design very easily. Furthermore, AM typically produces less waste than many traditional manufacturing techniques due to the process building a part layer by layer rather than removing unneeded material from a larger piece, resulting in a cheaper process. These freedoms make AM, and FFF in particular, highly prized among industrial producers. However, numerous challenges prevent the adoption of FFF by these companies. Particularly, a lack of available material options and anisotropic material properties lead to issues when attempting to produce a part targeted for use in a specific field. FFF is primarily commercially limited to two materials: polylactic acid (PLA) and acrylonitrile-butadiene-styrene (ABS) with a few other materials available in more specialized fields. However, essentially all these materials are limited to low use temperatures (less than 300 °C) and are primarily amorphous or with nearly negligible amounts of crystallinity. This severely limits the ability to tailor a printed part to a specific purpose and restricts the use of printed parts to applications requiring very low strengths. This is one reason why FFF, and most types of AM, is limited to the prototyping field rather than end-use applications. The other reason, anisotropic mechanical properties, is caused by the building methodology of AM. Creating a part layer by layer naturally introduces potential areas of weakness at the joining of the layers. If bulk properties are not recovered, the interlayer bond acts as a stress concentrator under load and will break before the bulk material. The work presented in this dissertation proposes methods to better understand the FFF system in order to address these two issues, leading to the optimization of the printing process and ability to expand the material catalog, particularly in the direction of high use temperature materials. The research discussed herein attempts to develop predictive models that may allow exploration into the FFF system which can be difficult to do experimentally, and by predicting the properties of a printed part, the models can guide future experimentation in FFF without the need for an extensive trial-and-error process. The work presented in this dissertation includes exploring the flow phenomena inside the FFF nozzle to determine extrudability as well as two-dimension and three-dimension heat transfer models with the goal of describing the viscoelastic, flow, diffusion, and stress development phenomena present in FFF.