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This is a pedagogical review of the ubiquitous 1/f^αnoises. The sections include the representation of 1/f^αnoise as a superposition of many relaxation processes; a discussion of the infinitely large fluctuations in the low frequency limit; 1/f^αnoise from diffusion processes; the measured statistical properties of 1/f^αnoises; 1/f^αnoises in self organized criticality; scaling laws in earthquake physics; 1/f noise in deterministic dynamical systems; an example of noise in a biophysical system; the numerical simulation of 1/f^αnoise; 1/f noise literature (including online resources).
E. Milotti (Fri,) studied this question.