Van der Waals (vdW) heterostructures represent a promising material platform with rich electronic and optical properties highly tunable via a wide selection of layer materials, electric doping, strain, and twist angle. Monolayers of transition metal dichalcogenide (TMD) semiconductors commonly show strong light-matter coupling and direct bandgaps from the infrared to the visible spectral range, making them promising candidates for various optoelectronic applications. Vertically stacking different TMD monolayers allows one to create TMD heterostructures with rich and tunable correlated electronic phases and optical properties. Among different methods to tune the properties of vdW heterostructures, the twist angle is the most unique parameter. In this dissertation, we investigated the twist angle dependent optical properties of interlayer excitons in TMD heterostructures. First, we studied the twist-angle dependent interlayer exciton lifetimes in MoSe₂/WSe₂ heterostructures. We found that the multiple resonances of interlayer excitons subject to strong confinement in the moiré potential. Their properties are consistent with the interpretation that these resonances are ground- and excited state excitons. Our experiments further revealed that the recombination dynamics of interlayer excitons depends strongly on the twist angle. For example, their lifetimes change from ~ 1 ns to hundreds of ns when the twist angle is increased from 1 to 3.5°. In collaboration with a theoretical group, we explored two mechanisms for this drastic dependence. First, a relative rotation between the two layers in real space translates to a rotation in the momentum space. As the twist angle is increased, the interlayer exciton transitions change from direct- to indirect transitions in the momentum spacing, leading to a longer lifetime. Second, the presence of moiré potential also has a significant impact on the lifetime, reducing its angle dependence by relaxing the requirement of momentum conservation. Next, we investigated the influence of moiré potential on interlayer exciton diffusion in MoSe₂/WSe₂ heterostructures. The interlayer exciton diffusion offers a unique channel of energy and information transport in TMD heterostructures. While early studies focused on how mobile excitons are in TMD heterostructures, we find that interlayer exciton diffusion is impeded in the presence of the moiré potential by comparing two types of samples: those prepared by mechanical exfoliation and those grown with chemical vapor deposition. We investigated multiple mechanically stacked samples with accurately controlled twist-angles. We showed that the interlayer exciton diffusion does not depend on the size of the moiré supercell in a simple and monotonic manner. These experiments provide an important and complementary view of the diffusion properties of interlayer excitons from those reported in the literature.