  Two-dimensional (2D) materials for their versatile band structures and
strictly 2D nature have attracted considerable attention over the past decade.
Graphene is a robust material for spintronics owing to its weak spin-orbit and
hyperfine interactions, while monolayer transition metal dichalcogenides (TMDs)
possess a Zeeman effect-like band splitting in which the spin and valley
degrees of freedom are nondegenerate. The surface states of topological
insulators (TIs) exhibit a spin-momentum locking that opens up the possibility
of controlling the spin degree of freedom in the absence of an external
magnetic field. Nanostructures made of these materials are also viable for use
in quantum computing applications involving the superposition and entanglement
of individual charge and spin quanta. In this article, we review a selection of
transport studies addressing the confinement and manipulation of charges in
nanostructures fabricated from various 2D materials. We supply the entry-level
knowledge for this field by first introducing the fundamental properties of 2D
bulk materials followed by the theoretical background relevant to the physics
of nanostructures. Subsequently, a historical review of experimental
development in this field is presented, from the early demonstration of
graphene nanodevices on SiO2 substrate to more recent progress in utilizing
hexagonal boron nitride to reduce substrate disorder. In the second part of
this article, we extend our discussion to TMDs and TI nanostructures. We aim to
outline the current challenges and suggest how future work will be geared
towards developing spin qubits in 2D materials.
