Scattering amplitudes of massless particles exhibit a remarkable simplicity, due to underlying worldsheet models known as Ambitwistor strings. While these models naturally manifest the BCJ colour/kinematics duality, they also lead to compact expressions for loop integrands from nodal Riemann spheres. This makes them ideally suited for studying the double-copy structure at loop-level, and we will use them to derive all-order representations for BCJ numerators at one loop. Time permitting, we will conclude with some comments on recent developments at higher loop order.