We argue that critical-like dynamics self-organize relatively easily in non-equilibrium systems, and that in biological systems such dynamics serve as templates upon which natural selection builds further elaborations. These critical-like states can be modified by natural selection in two fundamental ways, reflecting the selective advantage (if any) of heritable variations either among avalanche participants or among whole systems. First, reproducing (avalanching) units can differentiate, as units adopt systematic behavioural variations. Second, whole systems that are exposed to natural selection can become increasingly or decreasingly critical. We suggest that these interactions between SOC-like dynamics and natural selection have profound consequences for biological systems because they could have facilitated the evolution of division of labour, compartmentalization and computation, key features of biological systems. The logical conclusion of these ideas is that the fractal geometry of nature is anything but coincidental, and that natural selection is itself a fractal process, occurring on many temporal and spatial scales.