The significant development in the construction of microscale cell culture platforms and the interest in bioanalytical analysis have recently resulted in the emergence of a new concept of 'organ-on-a-chip' systems. Organ on-a-chip is a new three-dimensional (3D) in vitro microfabricated unit that contains a multichannel microfluidic cell culture. Even if many informative and useful data are obtained from animal models and in vitro assays, they are still limited for extrapolation to human systems during drug design and development. Only about 1 out of 10,000 compounds is processed in clinical trials for final approval. As being the first example of its kind, in this review, we summarize the current status and future challenges of this new concept that is a promising radical improvement in the drug-monitoring field. In addition, 3D-bioprinting methods used for the construction of organs-on-chips are outlined within the context in order to address the complexities in the field and show the various ways to create these semiartificial hybrid devices using a multidisciplinary approach comprising chemistry, biology, and engineering.