In this talk, I will present my recent result on global well-posedness and scattering for cubic Dirac equations on a weakly asymptotically flat backgrounds. To establish well-posedness in the full subcritical region: \(H^s(\mathbb R^3)\), \(s>1$, we prove the \(L^2_tL^\infty_x\(-endpoint Strichartz estimate for the half-Klein-Gordon equations. This is achieved by exploiting the phase space transform to construct an outgoing parametrix introduced by Metcalfe - Tataru. If time permits, I would also like to introduce my current ongoing project concerning global solutions to cubic Dirac and Dirac-Klein-Gordon systems on non-trapping asymptotically flat spacetimes using vector field methods.