Abstract: We review the transmission properties of carriers interacting with potential barriers in graphene. The tunneling of electrons and holes in quantum structures in graphene is found to display features that are in marked contrast with those of other systems. In particular, the interaction between the carriers with electrostatic potential barriers can be related to the propagation of electromagnetic waves in media with negative refraction indices, also known as metamaterials. This behavior becomes evident as one calculates the time evolution of wavepackets propagating across the barrier interface. In addition, we discuss the effect of trigonal warping on the tunneling through potential barriers.