The integration of nanotechnology into three-dimensional printing (3DP) offers huge potential and opportunities for the manufacturing of 3D engineered materials exhibiting optimized properties and multifunctionality. The literature relating to different 3DP techniques used to fabricate 3D structures at the macro- and microscale made of nanocomposite materials is reviewed here. The current state-of-the-art fabrication methods, their main characteristics (e.g., resolutions, advantages, limitations), the process parameters, and materials requirements are discussed. A comprehensive review is carried out on the use of metal- and carbon-based nanomaterials incorporated into polymers or hydrogels for the manufacturing of 3D structures, mostly at the microscale, using different 3D-printing techniques. Several methods, including but not limited to micro-stereolithography, extrusion-based direct-write technologies, inkjet-printing techniques, and popular powder-bed technology, are discussed. Various examples of 3D nanocomposite macro- and microstructures manufactured using different 3D-printing technologies for a wide range of domains such as microelectromechanical systems (MEMS), lab-on-a-chip, microfluidics, engineered materials and composites, microelectronics, tissue engineering, and biosystems are reviewed. Parallel advances on materials and techniques are still required in order to employ the full potential of 3D printing of multifunctional nanocomposites.