  The polarization analysis of optical transitions in monolayer and bilayer
transition-metal dichalcogenides provides invaluable information on the spin
and valley (pseudospin) degrees of freedom. To explain optical properties of a
given monolayer transition-metal dichalcogenide, one should consider (i) the
order of its spin-split conduction bands, (ii) whether intervalley scattering
is prone to phonon bottleneck, (iii) and whether valley mixing by electron-hole
exchange can take place. Using these principles, we present a consistent
physical picture that elucidates a variety of features in the optical spectra
of these materials. We explain the differences between optical transitions in
monolayer MoSe$_2$ and monolayer WSe$_2$, finding that indirect excitons in the
latter correspond to several low-energy optical transitions that so far were
attributed to excitons bound to impurities. A possible mechanism that can
explain the vanishing polarization in MoSe$_2$ is discussed. Finally, we
consider the effect of an out-of-plane electric field, showing that it can
reduce the initial polarization of bright excitons due to a Rashba-type
coupling with dark excitons.
