This review focuses on the advancements in additive manufacturing techniques that are utilized for fabricating bioceramic scaffolds and their characterizations leading to bone tissue regeneration. Bioscaffolds are made by mimicking the human bone structure, material composition, and properties. Calcium phosphate apatite materials are the most commonly used scaffold materials as they closely resemble live bone in their inorganic composition. The functionally graded scaffolds are fabricated by utilizing the right choice of the 3D printing method and material combinations to achieve the requirement of the bioscaffold. To tailor the physical, mechanical, and biological properties of the scaffold, certain materials are reinforced, doped, or coated to incorporate the functionality. The biomechanical loading conditions that involve flexion, torsion, and tension exerted on the implanted scaffold are discussed. The finite element analysis (FEA) technique is used to investigate the mechanical property of the scaffold before fabrication. This helps in reducing the actual number of samples used for testing. The FEA simulated results and the experimental result are compared. This review also highlights some of the challenges associated while processing the scaffold such as shrinkage, mechanical instability, cytotoxicity, and printability. In the end, the new materials that are evolved for tissue engineering applications are compiled and discussed.