  Beginning with the 'conventional' two-dimensional (2D) quantum wells (QWs)
based on III-V and II-VI semiconductors in the 1970s, to the recent
atomically-thin sheets of van der Waals materials such as 2D semiconducting
transition metal dichalcogenides (TMDCs) and 2D magnets, the research in 2D
materials is continuously evolving and providing new challenges. Magnetooptical
spectroscopy has played a significant role in this area of research, both from
fundamental physics and technological perspectives. A major challenge in 2D
semiconductors such as TMDCs is to understand their spin-valley-resolved
physics, and their implications in quantum computation and information
research. Since the discovery of valley Zeeman effects, deep insights into the
spin-valley physics of TMDCs and their heterostructures has emerged through
magnetooptical spectroscopy. In this perspective, we highlight the role of
magnetooptics in many milestones such as the discovery of interlayer excitons,
phase control between coherently-excited valleys, determination of
exciton-reduced masses, Bohr radii and binding energies, physics of the
optically-bright and dark excitons, trions, other many-body species such as
biexcitons and their phonon replicas in TMDC monolayers. The discussion
accompanies open questions, challenges and future prospects in the field
including comments on the magnetooptics of van der Waals heterostructures
involving TMDCs and 2D magnets.
