The evolution of electronic wave packets (WPs) through grain boundaries (GBs) of various structures in graphene was investigated by the numerical solution of the time-dependent Schrödinger equation. WPs were injected from a simulated STM tip placed above one of the grains. Electronic structure of the GBs was calculated by ab-initio and tight-binding methods. Two main factors governing the energy dependence of the transport have been identified: the misorientation angle of the two adjacent graphene grains and the atomic structure of the GB. In case of an ordered GB made of a periodic repetition of pentagon-heptagon pairs, it was found that the transport at high and low energies is mainly determined by the misorientation angle, but the transport around the Fermi energy is correlated with the electronic structure of the GB. A particular line defect with zero misorientation angle Lahiri et al., behaves as a metallic nanowire and shows electron-hole asymmetry for hot electrons or holes. To generate disordered GBs, found experimentally in CVD graphene samples, a Monte-Carlo-like procedure has been developed. Results show a reduced transport for the disordered GBs, primarily attributed to electronic localized states caused by C atoms with only two covalent bonds.