Gradient metasurfaces are 2-dimensional optical elements capable of manipulating light by imparting local, space-variant phase-changes on an incident electromagnetic wave. These surfaces have thus far been constructed from nanometallic optical antennas and high diffraction efficiencies have been limited to operation in reflection mode. We describe the experimental realization and operation of dielectric gradient metasurface optical elements capable of also achieving high efficiencies in transmission mode in the visible. Ultrathin gratings, lenses, and axicons have been realized by patterning a 100-nm-thin Si layer into a dense arrangement of Si nanobeam-antennas. The use of semiconductors can broaden the general applicability of gradient metasurfaces as they offer facile integration with electronics and can be realized by mature semiconductor fabrication technologies.