Three-dimensional (3D) printing offers the greatest potential to revolutionize the future of pharmaceutical manufacturing by overcoming challenges of conventional pharmaceutical operations and focusing design and production of dosage forms on the patient’s needs. Of the many technologies available, fusion deposition modelling (FDM) is considered of the lowest cost and higher reproducibility and accessibility, offering clear advantages in drug delivery. FDM requires in-house production of filaments of drug-containing thermoplastic polymers by hot-melt extrusion (HME), and the prospect of connecting the two technologies has been under investigation. The ability to integrate HME and FDM and predict and tailor the filaments’ properties will extend the range of printable polymers/formulations. Hence, this work revises the properties of the most common pharmaceutical-grade polymers used and their effect on extrudability, printability, and printing outcome, providing suitable processing windows for different raw materials. As a result, formulation selection will be more straightforward (considering the characteristics of drug and desired dosage form or release profile) and the processes setup will be more expedite (avoiding or mitigating typical processing issues), thus guaranteeing the success of both HME and FDM. Relevant techniques used to characterize filaments and 3D-printed dosage forms as an essential component for the evaluation of the quality output are also presented.