Novel additive manufacturing (AM) techniques and particularly 3D printing (3DP) have achieved a decade of success in pharmaceutical and biomedical fields. Highly innovative personalized therapeutical solutions may be designed and manufactured through a layer-by-layer approach starting from a digital model realized according to the needs of a specific patient or a patient group. The combination of patient-tailored drug dose, dosage, or diagnostic form (shape and size) and drug release adjustment has the potential to ensure the optimal patient therapy. Among the different 3D printing techniques, extrusion-based technologies, such as fused filament fabrication (FFF) and semi solid extrusion (SSE), are the most investigated for their high versatility, precision, feasibility, and cheapness. This review provides an overview on different 3DP techniques to produce personalized drug delivery systems and medical devices, highlighting, for each method, the critical printing process parameters, the main starting materials, as well as advantages and limitations. Furthermore, the recent developments of fused filament fabrication and semi solid extrusion 3DP are discussed. In this regard, the current state of the art, based on a detailed literature survey of the different 3D products printed via extrusion-based techniques, envisioning future directions in the clinical applications and diffusion of such systems, is summarized.