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Synthetic photonic materials created by engineering the profile of refractive index or gain/loss distribution, such as negative-index metamaterials or parity-time-symmetric structures, can exhibit electric and magnetic properties that cannot be found in natural materials, allowing for photonic devices with unprecedented functionalities. In this article, we discuss two directions along this line—non-Hermitian photonics and topological photonics—and their applications in nonreciprocal light transport when nonlinearities are introduced. Both types of synthetic structures have been demonstrated in systems involving judicious arrangement of optical elements, such as optical waveguides and resonators. They can exhibit a transition between different phases by adjusting certain parameters, such as the distribution of refractive index, loss, or gain. The unique features of such synthetic structures help realize nonreciprocal optical devices with high contrast, low operation threshold, and broad bandwidth. They provide promising opportunities to realize nonreciprocal structures for wave transport.