Graphene is an exceptionally thin semiconductor that consists of only one atomic layer of carbon atoms. The electrons in graphene live in a strictly two-dimensional (2D) world. In addition to this remarkable 2Dness, it is also peculiar that the behavior of the electrons in graphene is governed by the Dirac equation rather than the well known Schrödinger’s equation, leading to the discovery of several new physics phenomena. Such unusual properties of graphene have stirred up great excitements since it was first isolated in the lab about five years ago. In this thesis, we investigate the low temperature transport properties of the electrons and holes in several graphene based nano-devices. Overall, two topics are explored in this thesis. First we engineer an energy gap in graphene, which is naturally a zero-gap semiconductor, and further form quantum dot devices on the gapped graphene. The low temperature electronic transport properties of the confined electrons are then studied experimentally in such graphene dots. In a second project,we fabricated Josephson junction devices on graphene using a high critical field superconductor as leads. Here the goal is to research on the interactions between the electrons from graphene and the Cooper pairs from the superconductor in the quantum Hall regime.