In 2013, the “biofabrication window” was introduced to reflect the processing challenge for the fields of biofabrication and bioprinting. At that time, the lack of printable materials that could serve as cell‐laden bioinks, as well as the limitations of printing and assembly methods, presented a major constraint. However, recent developments have now resulted in the availability of a plethora of bioinks, new printing approaches, and the technological advancement of established techniques. Nevertheless, it remains largely unknown which materials and technical parameters are essential for the fabrication of intrinsically hierarchical cell–material constructs that truly mimic biologically functional tissue. In order to achieve this, it is urged that the field now shift its focus from materials and technologies toward the biological development of the resulting constructs. Therefore, herein, the recent material and technological advances since the introduction of the biofabrication window are briefly summarized, i.e., approaches how to generate shape, to then focus the discussion on how to acquire the biological function within this context. In particular, a vision of how biological function can evolve from the possibility to determine shape is outlined.