Recent developments in chip-based photonic quantum circuits have radically impacted quantum information processing. However, it is challenging for monolithic photonic platforms to meet the stringent demands of most quantum applications. Hybrid platforms combining different photonic technologies in a single functional unit have great potential to overcome the limitations of monolithic photonic circuits. Our Review summarizes the progress of hybrid quantum photonics integration, discusses important design considerations, including optical connectivity and operation conditions, and highlights several successful realizations of key physical resources for building a quantum teleporter. We conclude by discussing the roadmap for realizing future advanced large-scale hybrid devices, beyond the solid-state platform, which hold great potential for quantum information applications.