In this thesis we experimentally study charge transport through nano-devices made of graphene and topological insulators. In both these materials the low energy electronic states can be described by the Dirac equation. From systematic transport investigations of graphene devices on top of different substrates we found that both the charge mobility and the amount of charge density fluctuations in high-quality graphene devices are limited by the same microscopic mechanism. The experiments suggest that this mechanism originates from the presence of random strain fluctuations in graphene. In topological insulator nano-devices, our experiments show that charge transport can be modulated from electron to holes through the application of a gate voltage. Once in the presence of a magnetic field we also observe the occurrence of quantum oscillations for both charge polarities. Our experimental investigations on topological insulators conclusively show that transport at the surface of these materials is mediated by Dirac fermions.