In this talk, we present progress towards generalizing on-shell kinematics and color-kinematics duality to curved spacetimes. First, we define a perturbatively calculable quantity—the on-shell correlator—which furnishes a unified description of particle dynamics in curved spacetime. Specializing to the cases of flat and anti-de Sitter space, on-shell correlators coincide precisely with on-shell scattering amplitudes and boundary correlators respectively. We then introduce a notion of on-shell kinematics for symmetric spaces in which the corresponding on-shell momenta are built from isometry generators. Using this isometric language in AdS, we compute scalar correlators and give a field-theoretic derivation of color-kinematics duality for the nonlinear sigma model. Finally, we comment on possible extensions to spacetimes without symmetry.