Double copy is a method for constructing (perturbatively) scattering amplitudes in gravity from scattering amplitudes in gauge theory, and even has a catchy slogan: Gravity = (Gauge theory)^2. Despite is many uses, the status of double copy as a fundamental feature of perturbative field theories is poorly understood. In this talk I will describe how the robustness of double copy can be tested by considering the simplest scattering amplitudes on plane wave backgrounds. This makes use of several tools familiar from the study of QED in strong background fields. Despite various subtleties introduced by the non-trivial scattering background, it is clear that a notion of double copy does indeed exist.