We report a full study of graphene synthesis by CVD on Cu surface. Two CVD methods have been developed. The first is a static one, which yields monolayer of graphene at low pressure of methane in 3 minutes at 1000 C. The second one is an equimolar method which uses the same molar quantity of acetylene and carbon dioxide. Besides the catalytic action of the copper foil the graphene formation is boosted by the oxidative dehydrogenation (ODH) provoked by CO2. This method in 2 minutes results bilayer of graphene at low hydrocarbon pressure. The transfer of grapheme from the Cu foil has been elaborated in details using a polymer-assisted-transfer and Cu etching agents. Iron chloride and ammonium persulfate, were used as chemicals for etching. The products of both synthesis routes and grapheme transfers were extensively characterized by electron microscopies, Raman scattering, electrical resistivity, Seebeck coefficient, optical transmission, electron spin resonance and XPS. It turns out that the ODH introduces functional groups attached to the surface which have been identified as hydroxyl, epoxy and carboxyl. These groups are beneficial in sensor applications because they represent handles which could serve as docking cites for the targeted molecules. On the contrary, the etching agents affect the graphene both in terms of doping and introducing defects. Since these processes are less controllable their effect should be reduced. Several grapheme-based devices have been fabricated. For example, the ambipolar behavior and high quality of both single and bilayered materials have been illustrated by processing graphene field-effect transistor. Although functionalized, the bilayer graphene exhibits standard electrical behavior with respect to the change of channel dimensions and oxide thickness in transistor showing its suitability for sensor applications.