Electronic transport in low-dimensional systems such as carbon nanotubes, nanowires and more recently transition metal dichalcogenides (TMDs) and black phosphorus (BP) has attracted considerable attention over the years due to the unique properties that these classes of materials offer. In particular, the fact that these materials can be semiconducting with body thicknesses of sub-nanometers with appreciable carrier mobilities makes them relevant for various electronic applications. Consequently, many research activities have been focusing on the lateral transport through these structures, often in three-terminal device geometries. By utilizing a gate, ideal electrostatics conditions can be enabled in the low-dimensional semiconducting channel, due the aforementioned thin body, and field-effect transistors (FETs) can be built to explore their transport properties as a function of gate and drain voltage. In doing so, it was found that most devices behave as Schottky barrier transistors and that the total number of layers in case of 2D systems plays an important role for the effective bandgap of the FET, an aspect that I will discuss in greater detail in my talk. Multi-layer TMDs and BP are also particular in that the hybridization between layers is weak due to the fact that van der Waals interaction – rather than covalent or ionic bonds – is the “glue” between layers, making the system highly anisotropic for charge transport. In fact, this anisotropy is considered to be the key for the formation of so-called “atomically abrupt” p-n junctions, in particular in heterostructures from 2D materials. In my talk, I will discuss in how far lateral and vertical transport is rather entangled in many device geometries and will offer an alternative interpretation – other than an abrupt p-n junction – for transport data that show high current rectification ratios in vertical 2D heterostructures. Last, I will discuss a model to describe transport across multi-layer 2D structures that allows extracting the vertical transport mass in MoS₂ and WSe₂.