This article discusses the meaning and scope of biological hypercomputation (BH) that is to be considered as new research problem within the sciences of complexity. The framework here is computational, setting out that life is not a standard Turing Machine. Living systems, we claim, hypercompute, and we aim at understanding life not by what it is, but rather by what it does. The distinction is made between classical and nonclassical hypercomputation. We argue that living processes are nonclassical hypercomputation. BH implies then new computational models. Finally, we sketch out the possibilities, stances, and reach of BH. © 2014 Wiley Periodicals, Inc. Complexity 20: 8–18, 2014