As a result of progress in nanotechnology, smaller and smaller electronic circuits can be made. The stage of electrically contacting even a single molecule has now been reached. This stimulates both fundamental and applied research alike. Molecular electronics is hence a booming new field that draws a lot of attention. In this research project we have studied fundamental electrical transport properties of single molecules at low temperatures. In collaboration with chemists, a special kind of molecules has been synthesized for this purpose: molecular magnets. These molecules individually behave as tiny magnets. In this thesis, we describe the effect of the magnetic properties on the conductance of the molecule. Quantum mechanical effects play an important role in this respect. Furthermore, we looked at the conductance of a novel material system: graphene an atomic layer of graphite. Graphene is a semi-metal, in which electrons behave as relativistic, massless particles. By coupling graphene to superconducting electrodes, we were able to induce a supercurrent in graphene. The supercurrent in graphene can be tuned by a gate-electrode and hence the device behaves as a superconducting transistor. Our measurements provide new insights in the properties of this exotic material.