  Layered two-dimensional materials exhibit rich transport and optical
phenomena in twisted or lattice-incommensurate heterostructures with spatial
variations of interlayer hybridization arising from moir\'e interference
effects. Here, we report experimental and theoretical studies of excitons in
twisted heterobilayers and heterotrilayers of transition metal dichalcogenides.
Using MoSe$_2$-WSe$_2$ stacks as representative realizations of twisted van der
Waals bilayer and trilayer heterostructures, we observe contrasting optical
signatures and interpret them in the theoretical framework of interlayer
moir\'e excitons in different spin and valley configurations. We conclude that
the photoluminescence of MoSe$_2$-WSe$_2$ heterobilayer is consistent with
joint contributions from radiatively decaying valley-direct interlayer excitons
and phonon-assisted emission from momentum-indirect reservoirs that reside in
spatially distinct regions of moir\'e supercells, whereas the heterotrilayer
emission is entirely due to momentum-dark interlayer excitons of hybrid-layer
valleys. Our results highlight the profound role of interlayer hybridization
for transition metal dichalcogenide heterostacks and other realizations of
multi-layered semiconductor van der Waals heterostructures.
