Phosphorene and graphene have a tiny lattice mismatch along the armchair direction, which can result in an atomically sharp in-plane interface. The electronic properties of the lateral heterostructures of phosphorene/graphene are investigated by the first-principles method. Here, we demonstrate that the electronic properties of this type of heterostructure can be highly tunable by the quantum size effects and the externally applied electric field (Eext). At strong Eext, Dirac Fermions can be developed with Fermi velocities around one order smaller than that of graphene. Undoped and hydrogen doped configurations demonstrate three drastically different electronic phases, which reveal the strongly tunable potential of this type of heterostructure. Graphene is a naturally better electrode for phosphorene. The transport properties of two-probe devices of graphene/phosphorene/graphene exhibit tunnelling transport characteristics. Given these results, it is expected that in-plane heterostructures of phosphorene/graphene will present abundant opportunities for applications in optoelectronic and electronic devices.