The understanding of the electronic properties of nanoscale systems such as a single molecule is both of fundamental interest and important for the development of applications for these units. In my doctoral research, I have developed fabrication and measurement techniques and applied them to the study of single molecule conductance and nanoscale graphene devices. Using electromigrated breakjunctions to form nanometer-scale gaps, we measured the spindependent transport properties of individual N@C60 endofullerene molecules and observed a spin state transition as a function of magnetic field. In another system, we used the technique of repeatedly-formed breakjunctions to determine the conductance of the on and off isomers of individual photochromic dithienylethene molecules. Finally, in this thesis I also describe our current work-in-progress related to spin current injection into graphene using nanoscale non-magnetic electrodes.