I will show how to construct a Lagrangian based on a notion of minimal coupling that includes classical spin effects that is relevant to describe Kerr binaries in the post-Minkowski (PM) regime. Using such Lagrangian, I will derive expressions for the classical amplitude for the elastic 2—>2 process at 1PM and 2PM. I will then consider radiation reaction effects and their connection to the imaginary part of the 3PM spinning eikonal phase.