  Since its discovery, graphene has been a promising material for spintronics:
its low spin-orbit coupling, negligible hyperfine interaction, and high
electron mobility are obvious advantages for transporting spin information over
long distances. However, such outstanding transport properties also limit the
capability to engineer active spintronics, where strong spin-orbit coupling is
crucial for creating and manipulating spin currents. To this end, transition
metal dichalcogenides, which have larger spin-orbit coupling and good interface
matching, appear to be highly complementary materials for enhancing the
spin-dependent features of graphene while maintaining its superior charge
transport properties. In this review, we present the theoretical framework and
the experiments performed to detect and characterize the spin-orbit coupling
and spin currents in graphene/transition metal dichalcogenide heterostructures.
Specifically, we will concentrate on recent measurements of Hanle precession,
weak antilocalization and the spin Hall effect, and provide a comprehensive
theoretical description of the interconnection between these phenomena.
