In the past decade entropy theory for the actions of countable sofic groups has been developed starting with the work of Bowen and its extension by Kerr-Li. We extend their work by introducing locally compact sofic groups and developing entropy theory for actions of locally compact sofic groups – thereby producing measurable and topological dynamical invariants and establishing the variational principle. We compute the entropy for Poisson point processes on sofic groups and further establish the relationship between the entropies of an action of a group and its restriction to a lattice subgroup.