  Weyl fermions are one of the simplest objects that link ideas in geometry and
topology to highenergy physics and condensed matter physics. Although the
existence of Weyl fermions as elementary particles remains dubious, there is
mounting evidence of their existence as quasiparticles in certain condensed
matter systems. Such systems are termed Weyl semimetals (WSMs). Needless to
say, WSMs have emerged as a fascinating class of materials with unique
electronic properties, offering a rich playground for both fundamental research
and potential technological applications. This review examines recent
advancements in understanding electron transport in Weyl semimetals (WSMs). We
begin with a pedagogical introduction to the geometric and topological concepts
critical to understanding quantum transport in Weyl fermions. We then explore
chiral anomaly (CA), a defining feature of WSMs, and its impact on transport
phenomena such as longitudinal magnetoconductance (LMC) and the planar Hall
effect (PHE). The Maxwell-Boltzmann transport theory extended beyond the
standard relaxation-time approximation is then discussed in the context of Weyl
fermions, which is used to evaluate various transport properties. Attention is
also given to the effects of strain-induced gauge fields and external magnetic
fields in both time-reversal broken and inversion asymmetric inhomogeneous
WSMs. The review synthesizes theoretical insights, experimental observations,
and numerical simulations to provide a comprehensive understanding of the
complex transport behaviors in WSMs, aiming to bridge the gap between
theoretical predictions and experimental verification.
