Abstract: The double copy is an established relationship between gauge theories and gravity, which can be roughly summarised as GR ~ (Yang Mills)^2. In this talk, I will discuss surprising aspects of the double copy in three dimensions, where gauge theories can be both massive and gauge invariant. Using spinor-helicity techniques, I will discuss the idea of bootstrapping scattering amplitudes involving matter, gluons, and gravitons, which leads us to some interesting peculiarities of planar physics, such as the double copy of anyons and the Aharonov-Bohm phase.