In this paper we show the electronic transport and the quantum phase transitions that characterize the quantum Hall regime in graphene placed on SiO(2) substrates at magnetic fields up to 28 T and temperatures down to 4 K. The analysis of the temperature dependence of the Hall and longitudinal resistivity reveals intriguing non-universalities of the critical exponents of the plateau-insulator transition. These exponents depend on the type of disorder that governs the electrical transport and its characterization is important for the design and fabrication of novel graphene nano-devices.