We will discuss the relation between perturbative gauge theory and perturbative gravity, and look at how this relation extends to some exact classical solutions. First, we will review the double copy prescription that takes gauge theory amplitudes into gravity amplitudes, which has been crucial to progress in perturbative studies of supergravity. Then, we will see that the self-dual sectors provide an important insight into the relation between the theories. A key role is played by a kinematic algebraic structure mirroring the colour structure. Finally, we will see how these ideas extend to some exact classical solutions, namely black holes and plane waves. This leads to a relation of the type Schwarzschild as Coulomb charge squared.