Tissue engineering (TE) and regenerative medicine combines the principles of biomaterials and cell transplantation to develop new tissues and to promote endogenous regeneration. The 3D scaffolds and matrices appeared as assertive approaches to guide the development of functional engineered tissues. Moreover, these structures, alone or in combination with cells and bioactive agents, bring the mechanical support during in vitro cell growthand in vivo implantation. A diversity of biomaterials and manufacturing methods, including 3D bioprinting, have been used to create novel alternatives to traditional TE strategies. Natural and synthetic polymers, bioceramics, or combination of these as composites have been used. These biomaterial choices oscillate from long-lasting implants to bioresorbable scaffolding structures, shown both with and without cells, growth factors and other bioactive agents. Herein, the approaches and emerging technologies applied for scaffolds and matrices processing, and the tissue-specific considerations for scaffolding TE purposes are highlighted and discussed. Focus is on what has been used and tested in animal models. Some of the most recent designs that allowed creating “multifunctional” structures with complex biological functions and their effectiveness for different TE applications are also outlined.