Since the very first investigations of the electronic properties of graphene  the nature of the scattering disorder potential   has been shown to play an essential role in determining the carrier density  dependence of the conductance. Impurity scattering is characterized by two different times the transport and elastic scattering times  which are sensitive to the linear energy dispersion of graphene. The analysis of the  ratio between these two times  gives insight on the nature (neutral or charged) and range of  the scatterers. We  discuss how  to extract these two times from magneto-transport measurements and analyze their differences  in monolayer and bilayer Graphene in relation with the different symmetry properties of their band structure and wave functions. We show that whereas short range impurity scattering is the dominant mechanism limiting the classical transport,  phase coherent mesoscopic transport is very sensitive to long range disorder. In particular,  the formation of electron/hole puddles in the vicinity  of the charge neutrality point strongly affects the amplitude of the conductance fluctuations and the induced supercurrent in the presence of superconducting electrodes.