This talk is an introduction to the role of inverse semigroup theory in the study of $C^*$-algebras. Many $C^*$-algebras of interest are generated by a set of partial isometries closed under multiplication and adjoint - such a set is always an inverse semigroup. Here we give examples of such $C^*$-algebras, and discuss how properties of the generating inverse semigroup are reflected in the properties of the $C^*$-algebra. This is meant to be an expository talk, and no knowledge of $C^*$-algebras is assumed.