We present freestanding metasurfaces operating at optical frequencies with a total thickness of only 40 nm. The metasurfaces are fabricated by focused ion beam milling of nanovoids in a carbon film followed by thermal evaporation of gold and plasma ashing of the carbon film. As a first example, we demonstrate a metasurface lens based on resonant V-shaped nanovoids with a focal length of 1 mm. The second example is a metasurface phase plate consisting of appropriately oriented rectangular nanovoids that transform a Gaussian input beam into a Laguerre-Gaussian LG-1,0 mode.