Layered two-dimensional (2D) materials interact primarily via van der Waals bonding, which has created new opportunities for heterostructures that are not constrained by epitaxial lattice matching requirements [1]. However, since any passivated, dangling bond-free surface interacts with another via non-covalent forces, van der Waals heterostructures are not limited to 2D materials alone. In particular, 2D materials can be integrated with a diverse range of other materials, including those of different dimensionality, to form mixed-dimensional van der Waals heterostructures [2]. Furthermore, chemical functionalization provides additional opportunities for tailoring the properties of 2D materials [3] and the degree of coupling across heterointerfaces [4]. In this manner, a variety of optoelectronic and energy applications can be enhanced including photodetectors, optical emitters, supercapacitors, and batteries [5-7]. Due to their unique physics, mixed-dimensional heterostructures also enable unprecedented electronic and quantum functionality to be realized including gate-tunable Gaussian heterojunctions, neuromorphic memtransistors, and high-purity single-photon emitters [8-10]. In addition to technological implications for electronic and energy technologies, this talk will explore several fundamental issues including band alignment, doping, trap states, and charge/energy transfer across van der Waals heterointerfaces.