The book starts with a review of the established facts on the numerical simulations of binary neutron star mergers and simulations of short GRB jets that highlights the issues that need to be revised and further clarified, as the need to understand how the relativistic outflow was launched, what the initial structure of the outflow is, and how it evolved through its interaction with the binary ejecta. Constraints on a local population of faint short duration GRBs are then provided in light of the GW170817/GRB 170817A event at d 40 Mpc by considering statistical limits on a d Fermi Gamma-ray burst monitor data. In particular, it has been found that for 25% of GRBs, the photon index is shallower than -2/3, challenging the standard synchrotron emission scenario. The extent up to which the reverse shock component is detectable for short GRBs in radio wavelengths is analyzed. Results show that early, radio bright reverse shock is expected in many cases, but more rapid follow-up observational campaigns are required in order to test these predictions.