  In this review, we discuss the impact of interfaces and heterojuctions on the
electronic and thermoelectric transport properties of materials. We review
recent progress in understanding electronic transport in two-dimensional (2D)
materials ranging from graphene to transition metal dichalcogenides (TMDs),
their homojunctions (grain boundaries), lateral heterojunctions (such as
graphene/MoS$_2$ lateral interfaces), and vertical van der Waals (vdW)
heterostructures. We also review work in thermoelectric properties of 2D
heterojunctions, as well as their applications in creating devices such as
resonant tunneling diodes (RTDs). Lastly, we turn our focus to work in
three-dimensional (3D) heterostructures. While transport in 3D heterostructures
has been researched for several decades, here we review recent progress in
theory and simulation of quantum effects on transport via the Wigner and
non-equilibrium Green's functions (NEGF) approaches. These simulation
techniques have been successfully applied toward understanding the impact of
heterojunctions on the thermoelectric properties, with applications in energy
harvesting, and electron resonant tunneling, with applications in RTDs. We
conclude that tremendous progress has been made in both simulation and
experiments toward the goal of understanding transport in heterostructures and
this progress will soon be parlayed into improved energy converters and quantum
nanoelectronic devices.
