This thesis is concerned with the heating and electronic properties of nanoscale devices based on nanostructured graphene. As electronic devices scale down to nanometer dimensions, the operation depends on the detailed atomic structure. Emerging carbon nano-materials such as graphene, carbon nanotubes and graphene nanoribbons, exhibit promising electronic and heat transport properties. Much research addresses the electron mobility of pristine graphene devices. However, the thermal transport properties, as well as the effects of e-ph interaction, in nanoscale devices, based on nanostructured graphene, have received much less attention. This thesis contributes to the understanding of the thermal properties of nanostructured graphene. The computational analysis is based on DFT/TB-NEGF. We show how a regular nanoperforation of a graphene layer - a graphene antidot lattice (GAL) - may be a solution for making graphene a versatile material for electronics, as well as thermal management. One of the main results is that both electronic and thermal transport properties converge fast with the number of antidot rows between the leads. Increasing the antidot dimensions is found to reduce the thermal conductance relatively more than the electronic conductance. This trend may, together with other thermal scattering mechanisms such as disorder or isotopes, lead to fair thermoelectric performance of graphene with an otherwise high ability to conduct heat. We also propose two novel materials that can lead to pseudo 1D transport in graphene. These systems may be a favorable way of realizing electronic wires in integrated graphene circuits. Firstly, GAL waveguides, where a region of pristine graphene is sandwiched between GAL regions, utilize the electronic band gaps to obtain localized waveguide modes. Secondly, the increased chemical reactivity of graphene with a bend may be used to electronically isolate pseudo-ribbons by absorption of hydrogen along the bends. When a large current is passed through such nanostructures they will heat up due to the excitation of the local vibrations. This thesis further addresses effects of having a large finite bias voltage. In particular, we find that the electronic spectrum of nanostructured graphene features sharp variations in energy. Electronic resonances with a broadening on the scale of the phonon frequencies need a special treatment beyond the common praxis in theoretical modelling. There is a strong tendency to enter this regime in graphene technology due to the large phonon frequencies approaching 0:2 eV. The aim is to develop atomistic simulation methods that incorporate the effect from the electronic energy variation on the phonon energy scale in electronic conductance and local heating modelling. The methods we have developed are applied to graphene devices but are of much more general validity. We find a strongly nonlinear heating of phonons in a graphene nanoconstriction (GNC) with bias when the Fermi level is tuned close to a resonance in the electronic structure. The behavior is traced back to the presence of negatively damped phonons driven by the current. This effect may limit the stability and capacity of GNCs to carry high currents. Carbon nanosystems bridging electrically gated graphene electrodes may offer an interesting test-bed for these effects.