The introduction of spectral networks is motivated from the point of view of the construction of a non-abelianization map. Then spectral networks on ciliated surfaces are defined. We start with the simplest case of small spectral networks and then give a more general definition of non-degenerate spectral networks. Two different approaches to the construction of spectral networks are presented: the first is purely topological and combinatorial and works for ciliated surfaces S with punctures without any additional structure. The second, called WKB-spectral network, is rather analytic, with a choice of complex structure on S. Not all general spectral networks can be realized using this analytic construction. Further, we describe a path lifting rule using spectral networks which generalizes the usual path lifting property for non-ramified coverings, and which is homotopy invariant for ramified coverings.