Common cameras are only sensitive to the intensity of light, discarding an essential feature of a light wave: its phase profile or, equivalently, its wavefront profile. This Review focuses on a rising wavefront imaging technique called quadriwave lateral shearing interferometry (QLSI), based on the simple use of a 2dimensional diffraction grating, aka a cross-grating, in front of a regular camera. We detail the working principle of QLSI and its implementation on an optical microscope. We highlight its microscopy applications in bioimaging and nanophotonics, in particular for the characterization of living cells, nanoparticles, 2D materials, metasurfaces, microscale temperature gradients, and surface topography. Finally, we draw a critical comparison of QLSI with current quantitative phase microscopy techniques, namely, digital holography microscopy (DHM), spatial light interference microscopy (SLIM), and diffraction phase microscopy (DPM).