The eight-vertex model is an ubiquitous description that generalizes several spin systems, "ice-type" six-vertex models, and others. In a special "free-fermion" regime, it is known since the work of Fan, Lin, Wu in the late 60s that the model can be mapped to non-bipartite dimers. In this talk I will show how to transform these non-bipartite dimers into bipartite ones, which allows for a deep, rigorous study on generic planar graphs. I will mention a few consequences: computation of long-range correlations and critical exponents, critical regimes, and their "exact" application to Z-invariant regimes on isoradial graphs.