  What do societies, the Internet, and the human brain have in common? They are
all examples of complex relational systems, whose emerging behaviours are
largely determined by the non-trivial networks of interactions among their
constituents, namely individuals, computers, or neurons, rather than the
properties of the units themselves. In the last two decades, network scientists
have proposed models of increasing complexity to better understand real-world
systems. Only recently we have realised that multiplexity, i.e. the coexistence
of several types of interactions among the constituents of a complex system, is
responsible for substantial qualitative and quantitative differences in the
type and variety of behaviours that a complex system can exhibit. As a
consequence, multilayer and multiplex networks have become a hot topic in
complexity science. Here we provide an overview of some of the measures
proposed so far to characterise the structure of multiplex networks, and a
selection of models aiming at reproducing those structural properties and
quantifying their statistical significance. Focusing on a subset of relevant
topics, this brief review is a quite comprehensive introduction to the most
basic tools for the analysis of multiplex networks observed in the real-world.
The wide applicability of multiplex networks as a framework to model complex
systems in different fields, from biology to social sciences, and the
colloquial tone of the paper will make it an interesting read for researchers
working on both theoretical and experimental analysis of networked systems.
