Simply connected compact semisimple Lie groups are classified up to isomorphism by reduced crystallographic root systems together with their simply connected weight lattice. More generally, compact connected Lie groups are classified by a torus lattice, a semisimple root datum, and a finite subgroup of the product of the torus with the centre of the simply connected semisimple form; this finite subgroup must be central and its projections determine the allowed character lattice and the central quotient appearing in the compact connected structure theorem.