I will present our recent work on transient absorption microscopy (TAM) as a new tool to image dynamics with simultaneously high spatial (~ 200 nm) and temporal resolution (~ 200 fs) to investigate in carrier dynamics and transport of 2D nanostructures and heterostructures. I will first discuss such transient absorption microscopic studies individual 2D nanostructures. Femtosecond transient absorption microscopy was employed to study the environmental effects in carrier relaxation of graphene and exciton dynamics in atomically thin and semiconducting MoS2 crystals. By controlling the dielectric environment around monolayers of MoS2 crystals, our measurements provide a comprehensive understanding on intrinsic exciton dynamics, quantum confinement effect, exciton-phonon coupling, as well as how the dielectric environment alters optical properties and energy relaxation processes in these 2D crystals. Next I will discuss interfacial carrier generation and charge separation in 2D van der Waals heterostructures. A largely unexplored question is how interlayer coupling can be utilized to control interfacial charge generation and separation. However, the inherent spatial heterogeneity at the 2D interfaces presents a major difficulty in elucidating interfacial charge transfer dynamics in relation to interlayer coupling. To elude this difficulty, we employ TAM to directly image interfacial charge generation and separation at different interlayer coupling strengths in WS2-graphene heterostructure. An up to 4-fold enhancement in interfacial carrier generation with visible optical excitation is observed in WS2-graphene heterostructures, which we attribute to interfacial charge transfer transitions. Such interlayer states could also promote electrons from the graphene layer to the WS2 layer and allow carrier generation with excitation energy well below WS2 bandgap. Our results highlight the largely potential of heterostructures based on 2D nanostructures with atomically sharp interfaces as a platform for enhancing interfacial charge transfer and separation.