Three-dimensional (3D) printing, or rapid prototyping, is a fabrication technique that is used for various engineering applications with advantages such as mass production and fine tuning of spatial-dimensional properties. Recently, this fabrication method has been adopted for tissue engineering applications due to its ability to finely tune porosity and create precise, uniform, and repeatable structures. This review aims to introduce 3D printing applications in soft-tissue engineering and regenerative medicine including state-of-the-art scaffolds and key future challenges. Furthermore, 3D printing of individual cells, an evolution of traditional 3D printing technology which represents a cutting-edge technique for the creation of cell seeded scaffolds in vitro, is discussed. Key advances demonstrate the advantages of 3D printing, while also highlighting potential shortcomings to improve upon. It is clear that as 3D printing technology continues to develop, it will serve as a truly revolutionary means for fabrication of structures and materials for regenerative applications.