In this talk we will consider the challenging problem of the simulation of a multi-phase flow of immiscible fluids in fractured porous media. The discontinuities inside the rocks, called fractures, have a strong influence on the transport of the fluids within the rock medium, which usually has a lower permeability; however, the various distribution in position, dimension and orientation of the fractures inside the subsoil makes the computational domain highly challenging from the computational point of view. To reduce the number of unknowns, we will apply the Discrete Fracture Network (DFN) mathematical model to consider only the exchanges between the fractures, neglecting the surrounding medium. Moreover, to simplify the process of construction of a global conforming discretization on the complex network of fractures, we will consider the numerical scheme of the Virtual Element Method (VEM) which can handle general polygonal elements. A particular focus will be devoted on the numerical resolution of the two-phase (wetting and non-wetting) time-dependent flow problem with the iterative Implicit-Pressure-Implicit-Saturation method coupled with the VEM approach.