This Nordita program is devoted to amplitudes- and QFT-inspired analytic methods for gravity at all scales. The topics covered will include: recent progress for gravitational amplitudes, new perturbative/effective formalisms, and relations between gravity and gauge theory. Higher-order calculations for: post-Newtonian/Minkowskian and self-force corrections to the gravitational potential/wave emission, cosmological correlators and ultraviolet physics probing quantum gravity, and applications to string theory. Challenges of incorporating spin and tidal effects in general relativity, and scattering amplitudes for Kerr black holes. Flat space holography in the form of celestial amplitudes, asymptotic symmetries and gravitational memory.