  Complex systems consist of many interacting elements which participate in
some dynamical process. The activity of various elements is often different and
the fluctuation in the activity of an element grows monotonically with the
average activity. This relationship is often of the form "$fluctuations \approx
const.\times average^\alpha$", where the exponent $\alpha$ is predominantly in
the range $[1/2, 1]$. This power law has been observed in a very wide range of
disciplines, ranging from population dynamics through the Internet to the stock
market and it is often treated under the names \emph{Taylor's law} or
\emph{fluctuation scaling}. This review attempts to show how general the above
scaling relationship is by surveying the literature, as well as by reporting
some new empirical data and model calculations. We also show some basic
principles that can underlie the generality of the phenomenon. This is followed
by a mean-field framework based on sums of random variables. In this context
the emergence of fluctuation scaling is equivalent to some corresponding limit
theorems. In certain physical systems fluctuation scaling can be related to
finite size scaling.
