We present a review of the null affine formulation of Einstein’s equations, which allows them to be written in a hierarchical structure once suitable new variables are introduced. This framework naturally leads to a regularization of variables through its compactified version. After discussing the characteristic formulation in the spherically symmetric case and the description of extremal black holes within this approach, we will turn to stationary and axisymmetric spacetimes with spin. In the weak-spin limit, we will illustrate the method by characterizing the initial data on the future and past horizons and on the bifurcation sphere for the Kerr–Newman family. This new characterization yields coordinate systems that are regular not only in the exterior region but also in a neighborhood of both horizons.