We elucidate here process–structure–property relationships in implantable biomaterials processed by rapid prototyping approaches that are based on the principle of additive manufacturing. The conventional methods of fabrication of biomedical devices including freeze casting and sintering are limited because of difficulties in adaptation at the host site and mismatch in micro/macrostructure, mechanical and physical properties with the host tissue. Moreover, additive manufacturing has the advantage of fabricating patient-specific designs, which can be obtained from the computed tomography scan of the defect site. The discussion here comprises two parts – the first part briefly describes the evolution and underlying reasons that have led to 3D printing of scaffolds for tissue regeneration. The second part focuses on biocompatibility and mechanical properties of 3D scaffolds, fabricated by different approaches. The article concludes with a discussion on functionally graded scaffolds and vascularisation of 3D porous scaffolds that are envisaged to meet the requirements of the biomedical industry. In general, the mechanical properties of 3D printed scaffolds are governed by pore architecture, pore volume and percentage porosity. To ensure long-term endurance and the ability to withstand abrupt impact, it is important that the fabricated materials have a good combination of strength and energy absorption capability. While scaffolds with high interconnected porosity are preferred for tissue regeneration, such structures lack adequate mechanical strength and energy absorption capability. These mutually opposing requirements of high porosity and mechanical strength in conjunction with high energy absorption have hindered the application of 3D scaffolds as biomedical devices. In this regard, functionally graded 3D structures with high strength and energy absorption are potentially attractive for biomedical devices.