  We describe here recent work on the electronic properties, magnetoexcitons
and valley polarised electron gas in 2D crystals. Among 2D crystals, monolayer
$MoS_2$ has attracted significant attention as a direct-gap 2D semiconductor
analogue of graphene. The crystal structure of monolayer $MoS_2$ breaks
inversion symmetry and results in K valley selection rules allowing to address
individual valleys optically. Additionally, the band nesting near Q points is
responsible for enhancing the optical response of $MoS_2$.We show that at low
energies the electronic structure of $MoS_2$ is well approximated by the
massive Dirac Fermion model. We focus on the effect of magnetic field on
optical properties of $MoS_2$. We discuss the Landau level structure of massive
Dirac fermions in the two non-equivalent valleys and resulting valley Zeeman
splitting. The effects of electron-electron interaction on the valley Zeeman
splitting and on the magneto-exciton spectrum are described. We show the
changes in the absorption spectrum as the self-energy, electron-hole exchange
and correlation effects are included. Finally, we describe the valley-polarised
electron gas in $WS_2$ and its optical signature in finite magnetic fields.
