Van der Waals heterostructures are synthetic quantum materials composed of stacks of atomically thin two-dimensional (2D) layers. Because the electrons in the atomically thin 2D layers are exposed to layer-to-layer coupling, the properties of van der Waals heterostructures are defined not only by the constituent monolayers, but also by the interactions between the layers. Many fascinating electrical, optical and magnetic properties have recently been reported in different types of van der Waals heterostructures. In this Review, we focus on unique excited-state dynamics in transition metal...