  Magnetic topological semimetals (TSMs) are topological quantum materials with
broken time-reversal symmetry (TRS) and isolated nodal points or lines near the
Fermi level. Their topological properties would typically reveal from the
bulk-edge correspondence principle as nontrivial surface states such as Fermi
arcs or drumhead states, etc. Depending on the degeneracies and distribution of
the nodes in the crystal momentum space, TSMs are usually classified into Weyl
semimetals (WSMs), Dirac semimetals (DSMs), nodal-line semimetals (NLSMs),
triple-point semimetals (TPSMs), etc. In this review article, we present the
recent advances of magnetic TSMs from a computational perspective. We first
review the early predicted magnetic WSMs such as pyrochlore iridates and
HgCr2Se4, as well as the recently proposed Heusler, Kagome layers, and
honeycomb lattice WSMs. Then we discuss the recent developments of magnetic
DSMs, especially CuMnAs in Type-III and EuCd2As2 in Type-IV magnetic space
groups (MSGs). Then we introduce some magnetic NLSMs that are robust against
spin-orbit coupling (SOC), namely Fe3GeTe2 and LaCl (LaBr). Finally, we discuss
the prospects of magnetic TSMs and the interesting directions for future
research.
