  We explain that spectral networks are a unifying framework that incorporates
both shear (Fock-Goncharov) and length-twist (Fenchel-Nielsen) coordinate
systems on moduli spaces of flat SL(2,C) connections, in the following sense.
Given a spectral network W on a punctured Riemann surface C, we explain the
process of "abelianization" which relates flat SL(2)-connections (with an
additional structure called "W-framing") to flat C*-connections on a covering.
For any W, abelianization gives a construction of a local Darboux coordinate
system on the moduli space of W-framed flat connections. There are two special
types of spectral network, combinatorially dual to ideal triangulations and
pants decompositions; these two types of network lead to Fock-Goncharov and
Fenchel-Nielsen coordinates respectively.
