Mesoscopic systems have typical length scales between nanometres and microns. Their study has already vastly increased our knowledge about quantum physics, and their large potential for technological applications has been a strong driving force of this research.Over the past years, several new classes of mesoscopic systems have become a strong focus of condensed-matter physics. The aim of this project is to theoretically investigate such novel mesoscopic quantum systems and explore their potential for applications in nanoelectronic and spintronic devices.The systems under investigation will be (a) topological insulators and topological superconductors, (b) one-dimensional quantum wires, as well as (c) molecular quantum dots and nanoelectromechanical systems. Research on these systems, both theoretically and experimentally, has recently attracted a lot of attention even beyond the condensed-matter physics community.Within this project, I will (i) improve the theoretical understanding of each of these systems, (ii) propose realistic experimental setups and materials for their investigation, and (iii) develop ideas for future technological applications based on them. In particular, I will explore applications in the field of nanoelectronics, i.e., electronic components like wires and transistors which can be scaled down to nanometre sizes, and in the field of spintronics, where the spin degree of freedom of the electrons (instead of their charge) is exploited for applications. The project will strengthen the profile of the University of Luxembourg in condensed-matter physics. It will complement extremely well the existing activities at the Physics and Materials Science Research Unit. Moreover, my collaboration with the nanomaterials group at the CRP Lippmann and the future LIST will strengthen the ties with the University.