The framework of spectral networks was introduced as a proceure to compute BPS states of $4d$ $\mathcal N=2$ gauge theories. In this talk I will briefly review a generalization, known as exponential networks, which computes the enumerative invariants associated to special Lagrangians in certain Calabi-Yau threefolds. Applications include deriving the exact spectrum for the mirror of the local Hirzebruch surface. I will also sketch a new and more intuitive aspects of this framework, which elucidates the geometric meaning of the invariants in terms of elementary data of A-branes.