I will consider the structure of arbitrary spacetimes with a finite null boundary. The behaviour of the spacetime metric near the null boundary can be described using Gaussian null coordinates. This description reveals the universal structure on the boundary which is common to all spacetimes. Diffeomorphisms which preserve the coordinate form of the metric, or equivalently the universal structure, give rise to an infinite-dimensional symmetry algebra on the null surface, analogous to the BMS symmetries at null infinity. I show how the Wald-Zoupas prescription can be used to obtain the charges and fluxes associated with these symmetries in general relativity. As an example, we consider a causal diamond, and show that the symmetries imply infinitely-many conservation laws between the past and future null boundaries of a causal diamond in any spacetime satisfying the Einstein equation.