Asymmetric transport is an uneven physical response of counter-propagating signals that has significantly contributed to fundamental science and revolutionized advanced technology via a variety of significant devices including diodes and isolators in electronics, optics, acoustics, and heat transfer. Photonic metasurfaces are two-dimensional ultrathin arrays of engineered subwavelength meta-atoms, acting as local phase shifters, which unprecedentedly mold wavefronts at will with a virtually flat optical element. While such an architecture can be potentially harnessed to achieve two-way asymmetric response of free-space light at an optically thin flatland, asymmetric light transport cannot be fundamentally achieved by any linear system including linear metasurfaces. Here, we report asymmetric transport of free-space light at nonlinear metasurfaces, with harmonic generation, upon transmission and reflection. We also derive the nonlinear generalized Snell’s laws of reflection and refraction which were experimentally verified by angle-resolved anomalous refraction and reflection of the nonlinear light. The asymmetric transport at optically thin nonlinear interfaces is revealed by comparing the original path of light through the metasurface with its corresponding reversed propagation path. Such a two-way asymmetric response at metasurfaces opens a new paradigm for free-space ultrathin lightweight optical devices with one-way operation including unrivaled optical valves and diodes.