Three-dimensional (3D) topological semimetals (TSMs) have arrested special attentions as 3D analogues to graphene. The TSMs, for example, the Dirac and Weyl semimetals, show an array of intriguing physical properties arising from the electronic band structure topology, which have therefore been under immense investigations. Most of the known TSMs are nonmagnetic, whereas the magnetic TSMs are very few and remain less investigated. The interplay between magnetism and nontrivial topological states can result in exceptional physical properties, such as anomalous or even quantum anomalous Hall effect. In some TSMs with peculiar magnetic structures, the magnetic exchange could be tuned by application of an external magnetic field, which consequently can affect the topological properties. We review herein the family of antiferromagnetic semimetals EuCd_{2}Pn_{2} (Pn = As, Sb) which exhibit topological phase transitions induced by an external magnetic field through tuning the spin structures and hence the structure symmetries that are protecting the topological states. Besides, we will also briefly review several other related materials including the GdPtBi and MnBi_{2}Te_{4}. The herein discussed magnetism induced topological phase transition provides potential use in novel topological devices since the topological states could be conveniently controlled by external magnetic field. Furthermore, it also contributes important clues toward understanding the intimate relation between magnetism and topological states, which are instructive for designing new magnetic topological phases. At the end of this review, we also give a short perspective for the development of the magnetic TSMs.