  Topological semimetals are three-dimensional topological states of matter, in
which the conduction and valence bands touch at a finite number of points,
i.e., the Weyl nodes. Topological semimetals host paired monopoles and
antimonopoles of Berry curvature at the Weyl nodes and topologically protected
Fermi arcs at certain surfaces. We review our recent works on quantum transport
in topological semimetals, according to the strength of the magnetic field. At
weak magnetic fields, there are competitions between the positive
magnetoresistivity induced by the weak anti-localization effect and negative
magnetoresistivity related to the nontrivial Berry curvature. We propose a
fitting formula for the magnetoconductivity of the weak anti-localization. We
expect that the weak localization may by induced by inter- alley effects and
interaction effect, and occur in double-Weyl semimetals. For the negative
magnetoresistance induced by the nontrivial Berry curvature in topological
semimetals, we show the dependence of the negative magnetoresistance on the
carrier density. At strong magnetic fields, specifically, in the quantum limit,
the magnetoconduction depends on the type and range of the scattering potential
of disorder. The high-field positive magnetoconductivity may not be a
compelling signature of the chiral anomaly. For long-range Gaussian scattering
potential and half filling, the magnetoconductivity can be linear in the
quantum limit. A minimal conductivity is found at the Weyl nodes although the
density of states vanishes there.
