We review the particle production at the end of a first-order electroweak phase transition, showing that it may be rather generic in theories beyond the standard model. Dark matter may then be abundantly produced by this mechanism if it has a sizable coupling to the Higgs field. For an electroweak phase transition occuring at a temperature T_EW ~ 50-100 GeV, non-thermally generated dark matter with mass M_X > few TeV will survive thermalization after the phase transition, and could then potentially account for the observed dark matter relic density in scenarios where a thermal dark matter component is either too small or absent. Dark matter in these scenarios could then either be multi-TeV WIMPs whose relic abundace is mostly generated at the electroweak phase transition, or ``Baby-Zillas" with mass M_GUT >> M_X >> v_EW that never reach thermal equilibrium in the early universe.