Bioprinting techniques can be used for the in vitro fabrication of functional complex bio-structures. Thus, extensive research is being carried on the use of various techniques for the development of 3D cellular structures. This article focuses on direct writing techniques commonly used for the fabrication of cell structures. Three different types of bioprinting techniques are depicted: Laser-based bioprinting, ink-jet bioprinting and extrusion bioprinting. Further on, a special reference is made to the use of the bioprinting techniques for the fabrication of 2D and 3D liver model structures and liver on chip platforms. The field of liver tissue engineering has been rapidly developed, and a wide range of materials can be used for building novel functional liver structures. The focus on liver is due to its importance as one of the most critical organs on which to test new pharmaceuticals, as it is involved in many metabolic and detoxification processes, and the toxicity of the liver is often the cause of drug rejection.