  Monolayers of semiconducting transition metal dichalcogenides are
two-dimensional direct-gap systems which host tightly-bound excitons with an
internal degree of freedom corresponding to the valley of the constituting
carriers. Strong spin-orbit interaction and the resulting ordering of the
spin-split subbands in the valence and conduction bands makes the lowest-lying
excitons in WX$_2$ (X~being S or Se) spin-forbidden and optically dark. With
polarization-resolved photoluminescence experiments performed on a WSe$_2$
monolayer encapsulated in a hexagonal boron nitride, we show how the intrinsic
exchange interaction in combination with the applied in-plane and/or
out-of-plane magnetic fields enables one to probe and manipulate the valley
degree of freedom of the dark excitons.
