Local Unitarity allows to represent any differential cross-section as the integral of a finite integrand by realising locally the cancellations between real and virtual contributions guaranteed by the KLN theorem. It achieves that using local identities that hold at any perturbative order. As such, it is particularly suitable for numerical methods and, in general, for automation of fixed-order computations. The deeper connections between Local Unitarity and the original construction of the KLN theorem naturally lead to a novel treatment of initial state singularities that does not rely upon explicit amplitude-level factorisation and that connects more directly to the physics governing the interplay between the hadron description and the hard interaction.