  We prove that twisted groupoid C*-algebras are characterised, up to
isomorphism, by having Cartan semigroups, a natural generalisation of
normaliser semigroups of Cartan subalgebras. This extends the classic
Kumjian-Renault theory to general twisted \'etale groupoid C*-algebras, even
non-reduced C*-algebras of non-effective groupoids.
