  Complex systems are very often organized under the form of networks where
nodes and edges are embedded in space. Transportation and mobility networks,
Internet, mobile phone networks, power grids, social and contact networks,
neural networks, are all examples where space is relevant and where topology
alone does not contain all the information. Characterizing and understanding
the structure and the evolution of spatial networks is thus crucial for many
different fields ranging from urbanism to epidemiology. An important
consequence of space on networks is that there is a cost associated to the
length of edges which in turn has dramatic effects on the topological structure
of these networks. We will expose thoroughly the current state of our
understanding of how the spatial constraints affect the structure and
properties of these networks. We will review the most recent empirical
observations and the most important models of spatial networks. We will also
discuss various processes which take place on these spatial networks, such as
phase transitions, random walks, synchronization, navigation, resilience, and
disease spread.
