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 growth. Since any passivated, dangling bond-free surface interacts with another via noncovalent forces, 2D materials can be integrated with a diverse range of other materials, including those of different dimensionality, to form mixed-dimensional heterostructures. In order to efficiently explore the vast phase space for mixed-dimensional heterostructures, our laboratory employs solution-based additive assembly. By achieving high levels of nanomaterial monodispersity and printing fidelity, a variety of electronic and energy applications can be enhanced including photodetectors, optical emitters, supercapacitors, and batteries. Furthermore, by integrating multiple nanomaterials into heterostructures, unprecedented device functionality can be realized including anti-ambipolar transistors, gate-tunable Gaussian heterojunctions, and neuromorphic memtransistors. In addition to technological implications, this talk will explore several fundamental issues including band alignment, doping, trap states, and charge/energy transfer across heterointerfaces.