By numerically solving Einstein equations we are able to study the strong regime of gravity. In many astrophysical scenarios strong gravity plays a fundamental role such as compact binary systems: e.g. Black Hole binaries binary Neutron Stars and Black Hole-Neutron Star systems. In this talk I will discuss the simulations our group has been conducting in binary Neutron Star system where we can study the dynamics and gravitational radiation of the systems but also establish important connections with electromagnetic counterparts and even testing alternatives theories of gravity (i.e. Scalar-Tensor theories).