In recent years, we have established new theoretical and computational frameworks to allow predictive understanding of excited-state phenomena in functional materials of low dimensionality. In our recent study, we established a first-principles approach (Qiu et al., Nano Lett. 21 (2021)) to explore the role of exciton dispersion in the ballistic part of exciton diffusion, as a function of exciton dispersion in momentum space, within a propagating wavepacket picture. Our group is currently further developing and applying a GW-BSE scheme to include exciton-phonon interactions in the propagation (Cohen et al., arXiv:2305.04223). We are interested in the connection between semi-classical descriptions of exciton diffusion and our ab initio understanding of exciton transport (see Glazov et al., APL 121 (2022)), and working our way to establishing a first-principles assessment of underlying exciton dynamics in materials.