We present research results on the electronic transport in heterostructures based on p-type nickel oxide (NiO) with the n-type oxide semiconductors zinc oxide (ZnO) and cadmium oxide (CdO). NiO is a desirable candidate for application in (opto-)electronic devices. However, because of its small electron affinity, heterojunctions with most n-type oxide semiconductors exhibit conduction and valence band offsets at the heterointerface in excess of 1 eV. ZnO/NiO junctions exhibit a so called type-II band alignment, making electron-hole recombination the only process by which a current can vertically flow through the structure. These heterojunctions are nevertheless shown to be of practical use in efficient optoelectronic devices, as exemplified here by our UVconverting transparent solar cells. These devices, although exhibiting high conversion efficiencies, suffer from two light-activated recombination channels connected to the type-II interface, one of which we identify and analyse in more detail here. Furthermore, CdO/NiO contacts were studied a heterostructure with even larger band offsets such that a type-III band alignment is achieved. This situation theoretically enables the development of a 2-dimensional electronic system consisting of topologically protected states. We present experiments demonstrating that the CdO/NiO heterostructure indeed hosts a conductive layer absent in both materials when studied separately.