In this work, the influence of the underlying substrate on the mobility and electronic transport in graphene is evaluated by means of an ensemble Monte Carlo simulator. The substrates considered are h-BN, SiC, SiO2 and HfO2. The substrate type strongly affects the low-field mobility, particularly at room temperature; however, at low temperature the differences between supported graphene and suspended graphene tend to reduce due to a minor influence of surface polar phonon interactions. At room temperature, the anisotropy and inelasticity of SPP interactions yield lower average energies and larger drift velocities at high electric fields for all substrates. The overall results show the excellent performance (from the electronic transport point of view) of graphene on h-BN and SiC substrates at low and high temperatures.