Intrinsic Flat Convergence is a notion of convergence of Riemannian manifolds which has been applied to study sequences of time symmetric asymptotically flat initial data sets whose ADM mass is converging to zero. It is useful in settings where there is no smooth convergence due to the existence of gravity wells and/or black holes. After quickly reviewing the above results, I will present joint work with Sakovich developing Spacetime Intrinsic Flat Convergence of Lorentzian manifolds using the null distance defined jointly with Vega and the Cosmological Time function of Andersson-Galloway-Howard.