Electrical Resistivity Tomography (ERT) experiments are widely used for characterizing the natural environment because they easily provide a large number of data on a large extent and at various depths. These experiments are usually interpreted with forward models and inversion strategies that are well suited for equivalent porous medium representations. Dealing with fractured rocks requires using specific forward models, which are able to simulate the propagation of electric current flow in fracture networks that are embedded in conductive matrix-rock. Although such models have been recently developed, their integration into inversion strategies, and the definition of the inversion framework are still challenging. Here, we will start by showing how simple cases such as a single horizontal and vertical fracture can be handled by assuming the fracture position as known and inverting the fracture connectivity. We will then extend this to a regular network of fracture segments and will analyze various metrics of the inversion procedure, such as the convergence rate, resolution and depth of investigation. We will also discuss how defining prior information to improve the stochastic inversion strategy and future coupling with other characterization methods.