Flat optics has emerged as a key player in the area of structured light and its applications, owing to its subwavelength resolution, ease of integration, and compact footprint. Although its first generation has revolutionized conventional lenses and enabled anomalous refraction, new classes of meta-optics can now shape light and dark features of an optical field with an unprecedented level of complexity and multifunctionality. Here, we review these efforts with a focus on metasurfaces that use different properties of input light-angle of incidence and direction, polarization, phase distribution, wavelength, and nonlinear behavior-as optical knobs for tuning the output response. We discuss ongoing advances in this area as well as future challenges and prospects. These recent developments indicate that optically tunable flat optics is poised to advance adaptive camera systems, microscopes, holograms, and portable and wearable devices and may suggest new possibilities in optical communications and sensing.