Power-laws emerge in systems where several scales are simultaneously present. Biological, economic, and physical systems characterized by power-laws are currently investigated in several research areas. In this talk, I will discuss some examples of complex systems lacking a typical scale. Specifically, I will talk about
(i) base pair sequences of DNA in eukaryotes and prokaryotes
(ii) the time evolution of price and volatility of a financial asset traded in a financial market
(iii) the asymptotic time evolution of a class of quantum wave packets.
The presence of several scales in the investigated process defines the class of complexity of the phenomena considered. For example, the central limit theorem of probability theory cannot be applied in long-range power-law correlated systems. Indeed different statistical and theoretical tools need to be considered when one describes unpredictable space and/or time patterns of observables in these systems.

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