Stacking monolayers of transition metal dichalcogenides into a heterostructure with a finite twist-angle gives rise to artificial moire superlattices with a tunable periodicity. As a consequence, excitons experience a periodic potential, which can be exploited to tailor optoelectronic properties of these materials. While recent experimental studies have confirmed twist-angle dependent optical spectra, the microscopic origin of moire exciton resonances has not been fully clarified yet. Here, we combine first principle calculations with the excitonic density matrix formalism to study transitions between different moire exciton phases and their impact on optical properties of the twisted MoSe$_2$/WSe$_2$ heterostructure. At angles smaller than 2$^{circ}$ we find flat, moire trapped states for inter- and intralayer excitons. This moire exciton phase drastically changes into completely delocalized states already at 3$^{circ}$. We predict a linear and quadratic twist-angle dependence of excitonic resonances for the moire-trapped and delocalized exciton phase, respectively. Our work provides microscopic insights opening the possibility to tailor moire exciton phases in van der Waals superlattices.
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