3D printing represents a valuable alternative to traditional processing methods, clearly demonstrated by the promising results obtained in the manufacture of various products, such as scaffolds for regenerative medicine, artificial tissues and organs, electronics, components for the automotive industry, art objects and so on. This revolutionary technique showed unique capabilities for fabricating complex structures, with precisely controlled physical characteristics, facile tunable mechanical properties, biological functionality and easily customizable architecture. In this paper, we provide an overview of the main 3D-printing technologies currently employed in the case of poly (lactic acid) (PLA) and polyhydroxyalkanoates (PHA), two of the most important classes of thermoplastic aliphatic polyesters. Moreover, a short presentation of the main 3D-printing methods is briefly discussed. Both PLA and PHA, in the form of filaments or powder, proved to be suitable for the fabrication of artificial tissue or scaffolds for bone regeneration. The processability of PLA and PHB blends and composites fabricated through different 3D-printing techniques, their final characteristics and targeted applications in bioengineering are thoroughly reviewed.