  Recent results on the optical properties of mono- and few-layers of
semiconducting transition metal dichalcogenides are reviewed. Experimental
observations are presented and discussed in the frame of existing models,
highlighting the limits of our understanding in this emerging field of
research. We first introduce the representative band structure of these systems
and their interband optical transitions. The effect of an external magnetic
field is then considered to discuss Zeeman spectroscopy and optical pumping
experiments, both revealing phenomena related to the valley degree of freedom.
Finally, we discuss the observation of single photon emitters in different
types of layered materials, including wide band gap hexagonal boron nitride.
While going through these topics, we try to focus on open questions and on
experimental observations, which do not yet have a clear explanation.

Mesoscale and Nanoscale Physics