Metasurfaces utilizing engineered metallic nanostructures have recently emerged as an important means to manipulate the propagation of light waves in a prescribed manner. However, conventional metallic metasurfaces mainly efficiently work in the visible and near-infrared regime, and lack sufficient tunability. In this work, combining the pronounced plasmonic resonance of patterned graphene structures with a subwavelength-thick optical cavity, we propose and demonstrate novel graphene metasurfaces that manifest the potential to dynamically control the phase and amplitude of infrared light with very high efficiency. It is shown that the phase of the infrared light reflected from a simple graphene ribbon metasurface can span over almost the entire 2π range by changing the width of the graphene ribbons, while the amplitude of the reflection can be maintained at high values without significant variations. We successfully realize anomalous reflection, reflective focusing lenses, and non-diffracting Airy beams based on graphene metasurfaces. Our results open up a new paradigm of highly integrated photonic platforms for dynamic beam shaping and adaptive optics in the crucial infrared wavelength range.Metamaterials are rationally engineered composite materials with exotic properties not easily obtained or altogether unavailable in nature [1][2][3][4] . Metamaterials have attracted extensive attention from physicists, material scientists and engineers over the past decade, because they provide unprecedented opportunities to control light-matter interactions and light propagation in unusual ways. Recently, metasurfaces, a new class of two-dimensional (2D) metamaterials, have emerged at the frontier of metamaterials research [5][6][7] . In essence, metasurfaces introduce desired phase, amplitude, or polarizatin profiles by patterning planar subwavelength structures, offering additional, yet important degrees of freedom to mold the flow of light. Novel optical phenomena and devices based on metasurfaces include anomalous refraction or reflection 8,9 , strong spin-orbit interaction 10,11 , ultra-thin focusing or diverging lenses [12][13][14] , and holography 15,16 . Metasurfaces have also been applied to manipulate near-field surface waves [17][18][19][20] . Compared with their bulk metamaterial counterparts, the quasi-2D metasurfaces exhibit advantages of increased operation bandwidth and reduced losses 5,6 . These new designs are also compatible with planar, low-cost manufacturing and extremely suitable for device integration.So far, most metasurfaces rely on judiciously designed metallic nanostructures. At optical frequencies, metallic nanostructures with varied geometries support strong surface plasmon resonances, acting as local antennas in frequency selective surfaces (FSS) 21 that can eventually determine the direction, amplitude and polarization of refracted or reflected beams. However, it is known that the plasmonic response of metals becomes less pronounced as approaching mid-infrared or longer wavelengths because...