Biofabrication can be defined as the production of complex living and non-living biological products from raw materials such as living cells, molecules, extracellular matrices, and biomaterials. Cell and developmental biology, biomaterials science, and mechanical engineering are the main disciplines contributing to the emergence of biofabrication technology. The industrial potential of biofabrication technology is far beyond the traditional medically oriented tissue engineering and organ printing and, in the short term, it is essential for developing potentially highly predictive human cell- and tissue-based technologies for drug discovery, drug toxicity, environmental toxicology assays, and complex in vitro models of human development and diseases. In the long term, biofabrication can also contribute to the development of novel biotechnologies for sustainable energy production in the future biofuel industry and dramatically transform traditional animal-based agriculture by inventing 'animal-free' food, leather, and fur products. Thus, the broad spectrum of potential applications and rapidly growing arsenal of biofabrication methods strongly suggests that biofabrication can become a dominant technological platform and new paradigm for 21st century manufacturing. The main objectives of this review are defining biofabrication, outlining the most essential disciplines critical for emergence of this field, analysis of the evolving arsenal of biofabrication technologies and their potential practical applications, as well as a discussion of the common challenges being faced by biofabrication technologies, and the necessary conditions for the development of a global biofabrication research community and commercially successful biofabrication industry.