  History-dependent processes are ubiquitous in natural and social systems.
Many such stochastic processes, especially those that are associated with
complex systems, become more constrained as they unfold, meaning that their
sample-space, or their set of possible outcomes, reduces as they age. We
demonstrate that these sample-space reducing (SSR) processes necessarily lead
to Zipf's law in the rank distributions of their outcomes. We show that by
adding noise to SSR processes the corresponding rank distributions remain exact
power-laws, $p(x)\sim x^{-\lambda}$, where the exponent directly corresponds to
the mixing ratio of the SSR process and noise. This allows us to give a precise
meaning to the scaling exponent in terms of the degree to how much a given
process reduces its sample-space as it unfolds. Noisy SSR processes further
allow us to explain a wide range of scaling exponents in frequency
distributions ranging from $\alpha = 2$ to $\infty$. We discuss several
applications showing how SSR processes can be used to understand Zipf's law in
word frequencies, and how they are related to diffusion processes in directed
networks, or ageing processes such as in fragmentation processes. SSR processes
provide a new alternative to understand the origin of scaling in complex
systems without the recourse to multiplicative, preferential, or self-organised
critical processes.
