When a beam of 50‐GeV electrons collides head on with a terawatt laser pulse focused down to a few microns, extraordinary things can happen: Almost every electron plowing through the very dense laser field at the focus kicks a low‐energy photon up to multi‐GeV gamma‐ray energy, and lots of these “Compton‐backscattered” gammas then create electron‐positron pairs when they subsequently collide with laser photons coming toward them.