Polycaprolactone (PCL) has been extensively applied on tissue engineering because of its low-melting temperature, good processability, biodegradability, biocompatibility, mechanical resistance, and relatively low cost. The advance of additive manufacturing (AM) technologies in the past decade have boosted the fabrication of customized PCL products, with shorter processing time and absence of material waste. In this context, this review focuses on the use of AM techniques to produce PCL scaffolds for various tissue engineering applications, including bone, muscle, cartilage, skin, and cardiovascular tissue regeneration. The search for optimized geometry, porosity, interconnectivity, controlled degradation rate, and tailored mechanical properties are explored as a tool for enhancing PCL biocompatibility and bioactivity. In addition, rheological and thermal behavior is discussed in terms of filament and scaffold production. Finally, a roadmap for future research is outlined, including the combination of PCL struts with cell-laden hydrogels and 4D printing.