Graphene is a single atomic layer of carbon that is crystallized in the honeycomb configuration.  It has many unique properties that are of particular interest for the development of nanoscale electronic devices and sensors.  In particular, it is a semi-metal whose charge carrier density can be continuously tuned from n-type to p-type by applying an external electric field and has a linear energy-momentum dispersion in the vicinity of the Dirac point, which results in carrier mobilities that are higher than almost all semiconductors.  It also has a very large in-plane thermal conductivity and exceptional mechanical properties.  However, one of the primary issues that must be addressed before nanoscale electronic devices and sensors can be routinely fabricated is the development of methods for growing large-scale, device-quality, graphene films with uniform thickness at a relatively low cost.  An overview will be given of the techniques currently used for graphene synthesis and the research being done in my laboratory to synthesize single crystal films of graphene.