In this minireview, we outline the recent experimental and theoretical progress in the creation, characterization and manipulation of Majorana bound states (MBSs) in semiconductor-superconductor (SC) hybrid structures. After an introductory overview of the broader field we specifically focus on four of our recent projects in this direction. We show that the emergence of Fano resonances in the differential conductance in a normal lead-Majorana nanowire-quantum dot setup can be exploited to determine if a single MBS is contacted by the normal lead and the quantum dot providing an experimental test of the non-locality of MBSs. In the second project, the tunnel-coupling to two MBSs in an $s$-wave SC-Majorana nanowire Josephson junction (JJ) leads to a finite contribution of the MBSs to the equilibrium Josephson current probing directly the local spin-singlet contribution of the Majorana pair. We then shift our focus from MBSs forming in nanowire systems to MBSs forming in topological JJs. In a single sheet of buckled silicene with proximity induced superconductivity two local electric fields can be used to tune the junction between a topologically trivial and topologically non-trivial regime. In a Corbino geometry topological Josephson junction two MBSs harbored in Josephson vortices can rotate along the JJ and, in the course of this, will be exchanged periodically in the phase difference of the JJ. The tunneling current in a metal tip coupled to the JJ is shown to exhibit signs of the anyonic braiding phase of two MBSs.
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