The relationship between curvature and the causal geometry of solutions to the Einstein equations is a fundamental feature of General Relativity. The flux of curvature through a null hypersurface provides a natural way to measure the size of the curvature tensor. We have shown earlier, together with Rodnianski, that the radius of injectivity of a null hypersurface can be bounded from below only in terms of the size of the curvature flux through the hypersurface. I plan to discuss that result and show how it can be used to provide removal of singularity results. More precisely one can provide uniform bounds for the curvature tensor, depending only on smoothness assumptions in the past and the boundedness of the curvature flux.