In the tokamak scrape-off layer (SOL) the magnetic field lines are open, channeling particles and heat onto plasma facing components, and constraining their lifetime. This is a critical issue for ITER and future devices -- safe operation of fusion devices will require a better understanding of the SOL plasma dynamics \cite{Loarte2007}. The steady-state heat load onto the tokamak plasma facing components depends on the SOL width, which results from a balance between plasma injection from the core region, turbulent transport, and losses to the divertor or limiter. Recently, we have gained deep insights into the tokamak SOL dynamics in the inner-wall limited configuration (like the ITER start-up plasmas), by means of massively-parallel fluid electromagnetic turbulence simulations. SOL turbulence, in fact, is characterized by the presence of large amplitude meso-scale turbulence, which requires the use of a global, flux-driven approach. In order to address this turbulent system, we have developed GBS, a flux-driven global turbulence code implementing the drift-reduced Braginskii equations. Our investigations have pointed out, among the others, the mechanisms regulating the turbulence level and therefore the SOL width, the turbulent regimes, and the mechanisms driving the rotation in this region. GBS simulations at realistic size and plasma parameters display features normally observed in the SOL of limited discharges, for instance, low frequency drift-wave or ballooning turbulence, fluctuations with an amplitude of the order of 30 percent and a poloidal width of about 10 ion sound larmor radii. Moreover, we have recovered strongly skewed fluctuation PDFs revealing the presence of intermittent transport events. In the present talk, we address, in particular, (a) the mechanisms establishing the SOL width, which regulates the steady-state heat load and (b) the physics of coherent filamentary plasma structures (blobs) that can travel across the SOL carrying heat and particles. The simulated non-linear dynamics have been compared with analytical estimates, that have highlighted the key physics mechanisms at play in the SOL, and with experimental measurements taken in a number of tokamak worldwide, showing good agreement.