There are many different constructions which one can use to build $C^∗$-algebras from some kind of initial data. To name a few examples one can construct $C^∗$-algebras from groups, directed graphs, group actions by homeomorphisms and many other kinds of dynamical systems. There is a general framework for constructing $C^∗$-algebras using groupoids which generalises all these constructions. The groupoid $C^∗$-algebras have in recent years come to play an increasingly prominent role in the theory of $C^∗$-algebras. As in many other areas of mathematics, one of the natural questions one can ask about a mathematical object (like a $C^∗$-algebra) is if it can loosely speaking be decomposed into smaller and more manageable objects. One way to provide such a decomposition for $C^∗$-algebras is to describe all primitive ideals of the $C^∗$-algebra. In this talk I will report on a joint project with Sergey Neshveyev where we investigate the primitive ideals in groupoid $C^∗$-algebras and describe them for a large class of groupoids. The talk is aimed at non-experts.