The physical mechanisms limiting the mobility of graphene on SiO₂ are studied and printed graphene devices on a flexible substrate are realized. Intentional addition of charged scattering impurities is used to study the effects of charged impurities. Atomic-scale defects are created by noble-gas ions irradiation to study the effect of unitary scatterers. The results show that charged impurities and atomic-scale defects both lead to conductivity linear in density in graphene, with a scattering magnitude that agrees quantitatively with theoretical estimates. While charged impurities cause intravalley scattering and induce a small change in the minimum conductivity, defects in graphene scatter electrons between the valleys and suppress the minimum conductivity below the metallic limit. Temperature-dependent measurements show that longitudinal acoustic phonons in graphene produce a small resistivity which is linear in temperature and independent of carrier density; at higher temperatures, polar optical phonons of the SiO₂ substrate give rise to an activated, carrier density-dependent resistivity. Graphene is also made into high mobility transparent and flexible field effect device via the transfer-printing method. Together the results paint a complete picture of charge carrier transport in graphene on SiO₂ in the diffusive regime, and show the promise of graphene as a novel electronic material that have potential applications not only on conventional inorganic substrates, but also on flexible substrates.