  Two-dimensional (2D) van der Waals semiconductors represent the thinnest, air
stable semiconducting materials known. Their unique optical, electronic and
mechanical properties hold great potential for harnessing them as key
components in novel applications for electronics and optoelectronics. However,
the charge transport behavior in 2D semiconductors is more susceptible to
external surroundings (e.g. gaseous adsorbates from air and trapped charges in
substrates) and their electronic performance is generally lower than
corresponding bulk materials due to the fact that surface and bulk coincide. In
this article, we review recent progress on the charge transport properties and
carrier mobility engineering of 2D transition metal chalcogenides, with a
particular focus on the markedly high dependence of carrier mobility on
thickness. We unveil the origin of this unique thickness dependence and
elaborate the devised strategies to master it for carrier mobility
optimization. Specifically, physical and chemical methods towards the
optimization of the major factors influencing the extrinsic transport such as
electrode/semiconductor contacts, interfacial Coulomb impurities and atomic
defects are discussed. In particular, the use of \textit{ad-hoc} molecules
makes it possible to engineer the interface with the dielectric and heal the
vacancies in such materials. By casting fresh light onto the theoretical and
experimental works, we provide a guide for improving the electronic performance
of the 2D semiconductors, with the ultimate goal of achieving technologically
viable atomically thin (opto)electronics.
