Angular momentum is a basic and yet mysterious quantity. In this talk, I will discuss the angular momentum carried away by radiation in a classical scattering process. I will show new formulae for calculating angular momentum in electromagnetism and gravity and discuss several counter-intuitive features. The radiated linear/angular momentum can be used to bootstrap the dissipative force in binary inspiral, which is relevant to current and future gravitational-wave experiments. Combining the information from two-body scattering in GR, we bootstrap the binary dynamics to state-of-the-art precision without using the Einstein equations.