The advancement of high tech has raised the bar for precision interferometric imaging. In modern optics and biomedicine, label-free imaging techniques, which do not rely on traditional dyes or fluorescent markers, allow for 3D in situ observation and analysis of living cells, thereby promoting the development of quantitative phase microscopy. In the field of optical detection, there is an urgent need for on-site and real-time applications of interferometric systems, such as transient analysis of laser wavefronts, high-speed flow field detection, monitoring and control of adaptive optics, and high-precision optical system aberration analysis. These applications demand a compact, environmentally robust, and transient imaging interferometric system. To address these needs, this paper focuses on years of research in common-path shearing interferometry. The advantage of common-path interferometry is that it overcomes the instability of measurement results caused by environmental disturbances affecting the reference and test paths in dual-beam interferometry. The quadriwave lateral shearing interferometer can achieve transient phase imaging by capturing four sheared wavefronts in two orthogonal shearing directions from a single interferogram. This was enabled by a novel four-wave interferometric sensor (FIS4), composed of a randomly encoded grating and a phase chessboard based on the principle of quadriwave lateral shearing interferometry. The FIS4 interferometric wavefront sensor’s compact structure, which does not require a reference flat due to its self-interfering nature, effectively suppresses environmental vibrations. This review comprehensively introduces the principles, development history, wavefront reconstruction methods, and the wide applications of the FIS4 interferometric sensor based on quadriwave lateral shearing interferometry. With its unique advantages, such as compactness, robustness, high temporal resolution, and compatibility with existing microscopy systems, the FIS4 interferometric wavefront sensor shows broad application prospects in fields like biomedicine, optical measurement, and material characterization. The development of this technology not only provides new research tools for related fields but also opens up new possibilities for interdisciplinary innovation and discovery.