One of the most important open issue for the realization of a fusion reactor is the understanding of the turbulence that develops at the periphery of the device, in the region called the edge. Turbulence is the major cause of particles and energy losses and it is driven by the presence of plasma and magnetic field inhomogeneities. We present non-linear self-consistent simulations of the edge plasma dynamics and we interpret them by means of linear studies of the fluid equations modeling the system. The linear study points out the dependence of the instabilities growth rate and of their properties on the physical parameters of the system. We identify the regions where each instability dominates. By using the non-linear simulations, we then study how the plasma instabilities non-linearly develop and saturate.