Abstract: The electronic and optical properties of vertical heterostructures (HTSs) and lateral heterojunctions (HTJs) between (B,N)-codoped graphene (dop@Gr) and graphene (Gr), C3N, BC3 and h-BN monolayers are investigated using van der Waals density functional theory calculations. We have found that all the considered HTSs are energetically and thermally feasible at room temperature, and therefore they can be synthesized experimentally. The dop@Gr/Gr, BC3/dop@Gr and BN/dop@Gr HTSs are semiconductors with direct bandgaps of 0.1 eV, 80 meV and 1.23 eV, respectively, while the C3N/dop@Gr is a metal because of the strong interaction between dop@Gr and C3N layers. On the other hand, the dop@Gr-Gr and BN-dop@Gr HTJs are semiconductors, whereas the C3N-dop@Gr and BC3-dop@Gr HTJs are metals. The proposed HTSs can enhance the absorption of light in the whole wavelength range as compared to Gr and BN monolayers. The applied electric field or pressure strain changes the bandgaps of the HTSs and HTJs, indicating that these HTSs are highly promising for application in nanoscale multifunctional devices.