I will discuss several recent papers on the double copy. In the first part of the talk I will recap work extending the classical double copy correspondence to maximally symmetric curved spacetimes. I will describe how to construct the corresponding single and zeroth copies in asymptotically (A)dS spacetimes in Kerr-Schild form, and will clarify the interpretation of these copies using several examples, pointing out some peculiar features. In the second part of the talk, I will introduce Galileon fields, and will discuss how to generalize and extend the procedure relating gauge and gravity theories through color-kinematics replacements by showing that the classical perturbative double copy of pions corresponds to special Galileons. I will also show how to construct the single copy by mapping the bi-adjoint scalar radiation to the non-linear sigma model radiation through generalized color-kinematics replacements. Finally, if time permits, I will introduce work studying the double copy beyond leading order.