The active control of matter by strong electromagnetic fields is of growing importance, with applications all across the optical spectrum from the extreme-ultraviolet to the far-infrared. In recent years, phase-stable terahertz (THz) fields have shown tremendous potential in the observation and manipulation of elementary excitations in complex systems. The combination of concepts from attosecond science with advanced THz technology facilitates novel spectroscopic schemes, such as THz streaking. In general, driving charges at lower frequency enhances interaction energies and can promote drastically different dynamics. For example, mid-infrared excitation induces field-driven sub-cycle electron dynamics in nanostructure nearfields. Such frequency scalings will also impact nanostructure-based streaking, which has been theoretically proposed. Here, we experimentally demonstrate extensive control over nanostructure photoelectron emission using single-cycle THz transients. The locally enhanced THz near-field at a nanotip significantly amplifies or suppresses the detected photocurrent. We present field-driven streaking spectroscopy with spectral compression and expansion arising from electron propagation within the nanolocalized volume. THz near-field streaking produces rich spectrotemporal features and will yield unprecedented control over ultrashort electron pulses for imaging and spectroscopy.