Complex systems are characterised by specific time-dependent interactions among their many
constituents. As a consequence they often manifest rich, non-trivial and unexpected behaviour.
Examples arise both in the physical and non-physical worlds. The study of complex systems forms a
new interdisciplinary research area that cuts across physics, biology, ecology, economics,
sociology, and the humanities. In this paper we review the essence of complex systems from a
physicists’ point of view, and try to clarify what makes them conceptually different from systems
that are traditionally studied in physics. Our goal is to demonstrate how the dynamics of such
systems may be conceptualised in quantitative and predictive terms by extending notions from
statistical physics and how they can often be captured in a framework of co-evolving multiplex
network structures. We mention three areas of complex-systems science that are currently studied
extensively, the science of cities, dynamics of…