Current tissue engineering techniques have various drawbacks: they often incorporate uncontrolled and imprecise scaffold geometries, whereas the current conventional cell seeding techniques result mostly in random cell placement rather than uniform cell distribution. For the successful reconstruction of deficient tissue, new material engineering approaches have to be considered to overcome current limitations. An emerging method to produce complex biological products including cells or extracellular matrices in a controlled manner is a process called bioprinting or biofabrication, which effectively uses principles of rapid prototyping combined with cell-loaded biomaterials, typically hydrogels. 3D tissue printing is an approach to manufacture functional tissue layer-by-layer that could be transplanted in vivo after production. This method is especially advantageous for stem cells since a controlled environment can be created to influence cell growth and differentiation. Using printed tissue for biotechnological and pharmacological needs like in vitro drug-testing may lead to a revolution in the pharmaceutical industry since animal models could be partially replaced by biofabricated tissues mimicking human physiology and pathology. This would not only be a major advancement concerning rising ethical issues but would also have a measureable impact on economical aspects in this industry of today, where animal studies are very labor-intensive and therefore costly. In this review, current controlled material and cell positioning techniques are introduced highlighting approaches towards 3D tissue printing.