  Three-dimensional (3D) topological semimetals represent a new class of
topological matters. The study of this family of materials has been at the
frontiers of condensed matter physics, and many breakthroughs have been made.
Several topological semimetal phases, including Dirac semimetals (DSMs), Weyl
semimetals (WSMs), nodal-line semimetals (NLSMs), and triple-point semimetals,
have been theoretically predicted and experimentally demonstrated. The
low-energy excitation around the Dirac/Weyl nodal points, nodal line, or triply
degenerated nodal point can be viewed as emergent relativistic fermions.
Experimental studies have shown that relativistic fermions can result in a rich
variety of exotic transport properties, e.g., extremely large
magnetoresistance, the chiral anomaly, and the intrinsic anomalous Hall effect.
In this review, we first briefly introduce band structural characteristics of
each topological semimetal phase, then review the current studies on quantum
oscillations and exotic transport properties of various topological semimetals,
and finally provide a perspective of this area.
