As a fundamental optical approach to interferometry, Sagnac interference has been widely used for reflection manipulation, precision measurements, and spectral engineering in optical systems. Compared to other interferometry configurations, it offers attractive advantages by yielding a reduced system complexity without the need for phase control between different pathways, thus offering a high degree of stability against external disturbance and a low wavelength dependence. The advance of integration fabrication techniques has enabled chip-scale Sagnac interferometers with greatly reduced footprint and improved scalability compared to more conventional approaches implemented by spatial light or optical fiber devices. This facilitates a variety of integrated photonic devices with bidirectional light propagation, showing new features and capabilities compared to unidirectional-light-propagation devices such as Mach-Zehnder interferometers (MZIs) and ring resonators (RRs). This paper reviews functional integrated photonic devices based on Sagnac interference. First, the basic theory of integrated Sagnac interference devices is introduced, together with comparisons to other integrated photonic building blocks such as MZIs, RRs, photonic crystal cavities, and Bragg gratings. Next, the applications of Sagnac interference in integrated photonics, including reflection mirrors, optical gyroscopes, basic filters, wavelength (de)interleavers, optical analogues of quantum physics, and others, are systematically reviewed. Finally, the open challenges and future perspectives are discussed.