  Over the past two decades, complex network theory provided the ideal
framework for investigating the intimate relationships between the topological
properties characterizing the wiring of connections among a system's unitary
components and its emergent synchronized functioning. An increased number of
setups from the real world found therefore a representation in term of graphs,
while more and more sophisticated methods were developed with the aim of
furnishing a realistic description of the connectivity patterns under study. In
particular, a significant number of systems in physics, biology and social
science features a time-varying nature of the interactions among their units.
We here give a comprehensive review of the major results obtained by
contemporary studies on the emergence of synchronization in time-varying
networks. In particular, two paradigmatic frameworks will be described in
details. The first encompasses those systems where the time dependence of the
nodes' connections is due to adaptation, external forces, or any other process
affecting each of the links of the network. The second framework, instead,
corresponds to the case in which the structural evolution of the graph is due
to the movement of the nodes, or agents, in physical spaces and to the fact
that interactions may be ruled by space-dependent laws in a way that
connections are continuously switched on and off in the course of the time.
Finally, our report ends with a short discussion on promising directions and
open problems for future studies.
