Just as groups are algebraic models of symmetry, inverse semigroups capture the notion of partial symmetry. One of the major results in algebraic semigroup theory is the ESN (Ehresmann-Schein-Nambooripad) Theorem which describes the structure of inverse semigroups using groupoids. In this talk, we discuss how we can generalise this to the class of regular $\star$-semigroups. Just like inverse semigroups, regular $\star$-semigroups have an involution to capture the symmetry, but their idempotents no longer form a semilattice. Natural examples of regular $\star$-semigroups include the partition, Brauer and Temperley-Lieb monoids, among other diagram monoids.  By focussing on the \emph{projection algebra} structure of a regular $\star$-semigroup, we obtain a category isomorphism between semigroups and certain ordered groupoids, just as in the ESN theorem. By applying this result, we construct the classical maximum fundamental regular $\star$-semigroup and also a new free idempotent generated regular $\star$-semigroup. This is a joint work with James East.