Initiated by the discovery of topological insulators, topologically non-trivial materials have attracted immense interest in the physics community in the past decade. One of the latest additions to the field, the material class of topological semimetals, has grown at an extremely fast rate. While the prototype topological semimetal, graphene, has been known for a while, the first 3D analogues of graphene have only been discovered recently. This review, written from a chemistry perspective, intends to make the growing field of topological semimetals accessible to the wider community of materials scientists and scholars from related disciplines. To this end, we describe key features of topological semimetals, embedded in their electronic structure, and how they can be achieved based on chemical principles. We introduce the different classes of topological semimetals and review their salient representatives. Finally, selected properties and potential applications of these materials are discussed.