Biological systems reach hierarchical complexity that has no counterpart outside the realm of biology. Undoubtedly, biological entities obey the fundamental physical laws. Can today’s physics provide an explanatory framework for understanding the evolution of biological complexity? We argue here that the physical foundation for understanding the origin and evolution of complexity can be envisaged at the interface between the theory of frustrated states resulting in pattern formation in glass-like media and the theory of self-organized criticality (SOC). On the one hand, SOC has been shown to emerge in spin glass systems of high dimensionality. On the other hand, SOC is often viewed as the most appropriate physical description of evolutionary transitions in biology. We unify these two faces of SOC by showing that emergence of complex features in biological evolution typically if not always is triggered by frustration that is caused by competing interactions at different organizational levels. Competing interactions and frustrated states permeate biology at all organizational levels and are tightly linked to the ubiquitous competition for limiting resources. This perspective extends from the comparatively simple phenomena occurring in glasses to large-scale events of biological evolution, such as major evolutionary transitions. We therefore submit that frustration caused by competing interactions in multidimensional systems is the general driving force behind the emergence of complexity, within and beyond the domain of biology.