The advent of the miniaturization approach has influenced the research trends in almost all disciplines. Bioengineering is one of the fields benefiting from the new possibilities of microfabrication techniques, especially in cell and tissue culture, disease modeling, and drug discovery. The limitations of existing 2D cell culture techniques, the high time and cost requirements, and the considerable failure rates have led to the idea of 3D cell culture environments capable of providing physiologically relevant tissue functions in vitro. Organ-on-chips are microfluidic devices used in this context as a potential alternative to in vivo animal testing to reduce the cost and time required for drug evaluation. This emerging technology contributes significantly to the development of various research areas, including, but not limited to, tissue engineering and drug discovery. However, it also brings many challenges. Further development of the technology requires interdisciplinary studies as some problems are associated with the materials and their manufacturing techniques. Therefore, in this paper, organ-on-chip technologies are presented, focusing on the design and fabrication requirements. Then, state-of-the-art materials and microfabrication techniques are described in detail to show their advantages and also their limitations. A comparison and identification of gaps for current use and further studies are therefore the subject of the final discussion.