3D printed neat thermoplastic polymers (TPs) and continuous fiber-reinforced thermoplastic composites (CFRTPCs) by fused filament fabrication (FFF) are becoming attractive materials for numerous applications. However, the structure of these materials exhibits interfaces at different scales, engendering non-optimal mechanical properties. The first part of the review presents a description of these interfaces and highlights the different strategies to improve interfacial bonding. The actual knowledge on the structural aspects of the thermoplastic matrix is also summarized in this contribution with a focus on crystallization and orientation. The research to be tackled to further improve the structural properties of the 3D printed materials is identified. The second part of the review provides an overview of structural health monitoring technologies relying on the use of fiber Bragg grating sensors, strain gauge sensors and self-sensing. After a brief discussion on these three technologies, the needed research to further stimulate the development of FFF is identified. Finally, in the third part of this contribution the technology landscape of FFF processes for CFRTPCs is provided, including the future trends.