Spectral networks are a combinatorial tool consisting of labelled lines on a Riemann surface. They have a surprising amount of applications and are intimately linked to non-Abelianization of flat connections, Fock–Goncharov cluster coordinates, exact WKB theory, etc. After reviewing this story for the SL(2) and SL(3) cases, I will describe this is in detail for the group $G_2$. Time permitting, I will give as an application a concrete parametrization of the nonabelian Hodge correspondence for the Hitchin component of the split real form of $G_2$. This is joint work with Andy Neitzke.