Quality factors as high as 2,500 can be achieved for subwavelength phase gradient metasurfaces. Dielectric microcavities with quality factors (Q-factors) in the thousands to billions markedly enhance light-matter interactions, with applications spanning high-efficiency on-chip lasing, frequency comb generation and modulation and sensitive molecular detection. However, as the dimensions of dielectric cavities are reduced to subwavelength scales, their resonant modes begin to scatter light into many spatial channels. Such enhanced scattering is a powerful tool for light manipulation, but also leads to high radiative loss rates and commensurately lowQ-factors, generally of order ten. Here, we describe and experimentally demonstrate a strategy for the generation of highQ-factor resonances in subwavelength-thick phase gradient metasurfaces. By including subtle structural perturbations in individual metasurface elements, resonances are created that weakly couple free-space light into otherwise bound and spatially localized modes. Our metasurface can achieveQ-factors >2,500 while beam steering light to particular directions. High-Qbeam splitters are also demonstrated. With high-Qmetasurfaces, the optical transfer function, near-field intensity and resonant line shape can all be rationally designed, providing a foundation for efficient, free-space-reconfigurable and nonlinear nanophotonics.