We present a systematic numerical relativity study of the mass ejection and the associated electromagnetic transients and nucleosynthesis from binary neutron star (NS) mergers. We find that a few 10−3 M ⊙ of material is ejected dynamically during the mergers. The amount and the properties of these outflows depend on binary parameters and on the NS equation of state (EOS). A small fraction of these ejecta, typically ~10−6 M ⊙, is accelerated by shocks formed shortly after merger to velocities larger than 0.6c and produces bright radio flares on timescales of weeks, months, or years after merger. Their observation could constrain the strength with which the NSs bounce after merger and, consequently, the EOS of matter at extreme densities. The dynamical ejecta robustly produce second and third r-process peak nuclei with relative isotopic abundances close to solar. The production of light r-process elements is instead sensitive to the binary mass ratio and the neutrino radiation treatment. Accretion disks of up to ~0.2 M ⊙ are formed after merger, depending on the lifetime of the remnant. In most cases, neutrino- and viscously driven winds from these disks dominate the overall outflow. Finally, we generate synthetic kilonova light curves and find that kilonovae depend on the merger outcome and could be used to constrain the NS EOS.