Neutrinos are among the most mysterious particles known in fundamental physics, not least because interact extremely weakly with other matter and are therefore very hard to detect. In the Standard Model of particle physics, neutrinos come in three different types (called "flavours"), but for several years, the hypothesis that more than these three neutrino flavours exist, has received considerable attention. One of the foremost goals of the project "nuDirection" is to address the possible existence of a fourth, "sterile", neutrino from the theoretical and phenomenological side. By interpreting and combing data from a large number of experiments, we assess the viability of scenarios with more than three neutrino flavours. We also disucss such scenarios in a broader context, encompassing in particular their consequences for cosmology and astrophysics. Beyond sterile neutrinos, we explore more general extensions of the neutrino sector of the standard model. Several controversial experimental hints exist for neutrino physics beyond the three-flavour paradigm, and if any of these should be confirmed, it would constitute a major breakthrough. Even in the absence of such a discovery, the results from this project will significantly improve our understanding of neutrino physics. This will be crucial in the context of the future experimental program in particle physics, especially in view of multi-billion euro investment in facilities in the US and in Japan.