The talk reports on recent progress in amplitude computations for broad classes of N=2 Maxwell-Einstein and Yang-Mills-Einstein supergravities, using the framework provided by color/kinematics duality and the double-copy construction. After a review of the main theoretical tools employed in the computations, we discuss the extension of the double-copy construction to a particular infinite family of N=2 Maxwell-Einstein supergravities in four and five dimensions and show that the global symmetries of these theories can easily be gauged, giving the amplitudes of the corresponding Yang-Mills-Einstein supergravities. Finally, we discuss how the construction can be modified to describe spontaneous symmetry breaking and present examples at one loop.