The fused deposition modeling (FDM) process, an extrusion-based 3D printing technology, enables the manufacture of complex geometrical elements. This technology employs diverse materials, including thermoplastic polymers and composites as well as recycled resins to encourage sustainable growth. FDM is used in a variety of industrial fields, including automotive, biomedical, and textiles, as a rapid prototyping method to reduce costs and shorten production time, or to develop items with detailed designs and high precision. The main phases of this technology include the feeding of solid filament into a molten chamber, capillary flow of a non-Newtonian fluid through a nozzle, layer deposition on the support base, and layer-to-layer adhesion. The viscoelastic properties of processed materials are essential in each of the FDM steps: (i) predicting the printability of the melted material during FDM extrusion and ensuring a continuous flow across the nozzle; (ii) controlling the deposition process of the molten filament on the print bed and avoiding fast material leakage and loss of precision in the molded part; and (iii) ensuring layer adhesion in the subsequent consolidation phase. Regarding this framework, this work aimed to collect knowledge on FDM extrusion and on different types of rheological properties in order to forecast the performance of thermoplastics.