Septins are cytoskeletal proteins interacting with the inner plasma membrane and other cytoskeletal partners. Being key in membrane remodeling processes, they often localize at specific micrometric curvatures. To analyze the behavior of human septins at the membrane and decouple their role from other partners, we used a combination of bottom-up in vitro methods. We assayed their ultrastructural organization, their curvature sensitivity, as well as their role in membrane reshaping. On membranes, human septins organize into a two-layered mesh of orthogonal filaments, instead of generating parallel sheets of filaments observed for budding yeast septins. This peculiar mesh organization is sensitive to micrometric curvature and drives membrane reshaping as well. The observed membrane deformations together with the filamentous organization are recapitulated in a coarse-grained computed simulation to understand their mechanisms. Our results highlight the specific organization and behavior of animal septins at the membrane as opposed to those of fungal proteins.