The last 10 years have witnessed an impressive amount of works aiming at the development of thin metamaterials for controlling the wavefront of light, and thus realize planar photonics also referred as flat optics or metaoptics. The concept of metasurface is at the heart of almost all the discoveries in this domain. Metasurfaces are arrays of subwavelength-spaced and optically thin optical elements, which enable new physics and phenomena that are distinctly different from those observed in three-dimensional bulk metamaterials. We present here our recent activities and achievements in relation with the design of metasurfaces, which are concerned with two topics: on one hand, we study numerical characterization approaches that are well suited to the multiscale nature of metasurfaces; on the other hand, we develop inverse design strategies for discovering non-classical metasurface configurations for a target optical functionality. These two topics are addressed in the context of a multidisciplinary collaborative project, which involve computational scientists and physicists. In particular, we apply the proposed numerical methodologies to the design of phase gradient metasurfaces and light front shaping metalenses. In some cases, the numerically designed metasurfaces have been frabricated and experimentally characterized to confirm their predicted performances.