Topological phases of matter are an exotic phenomenon in modern condensed matter physics, which has attracted much attention due to the unique boundary states and transport properties. Recently, this topological concept in electronic materials has been exploited in many other fields of physics. Motivated by designing and controlling the behavior of electromagnetic waves in optical, microwave, and sound frequencies, topological photonics emerges as a rapid growing research field. Due to the flexibility and diversity of superconducting quantum circuits system, it is a promising platform to realize exotic topological phases of matter and to probe and explore topologically‐protected effects in new ways. Here, theoretical and experimental advances of topological photonics on superconducting quantum circuits—via the experimentally demonstrated parametric tunable coupling techniques, including using of the superconducting transmission line resonator, superconducting qubits, and their coupled system—are reviewed. On superconducting circuits, the flexible interactions and intrinsic nonlinearity make topological photonics in this system not only a simple photonic analog of topological effects for novel devices, but also a realm of exotic but less‐explored fundamental physics.