Ultrafast transport of electrons in semiconductors lies at the heart of high-speed electronics, electro-optics and fundamental solid-state physics. Intense phase-locked terahertz (THz) pulses at photon energies far below electronic interband resonances may serve as a precisely adjustable alternating bias, strongly exceeding d.c. breakdown voltages. Here, we exploit the near-field enhancement in gold metamaterial structures on undoped bulk GaAs, driven by few-cycle THz transients centered at 1 THz, to bias the semiconductor substrate with field amplitudes exceeding 12 MV/cm. Such fields correspond to a potential drop of the bandgap energy over a distance of only two unit cells. In this extremely off-resonant scenario characterized by a Keldysh parameter of γK ≈ 0.02, massive interband Zener tunneling injects a sizeable carrier density exceeding 1019 cm-3, and strong photoluminescence results. At a center frequency of 30 THz, THz transients with peak fields of 72 MV/cm analogously excite carriers in a bulk, semiconducting GaSe crystal, without metamaterial. Here, in contrast, we are able to drive coherent interband polarization and furthermore dynamical Bloch oscillations of electrons in the conduction band, on femtosecond time scales. The dynamics entail the generation of absolutely phase-stable high-harmonic transients containing spectral components up to the 22nd order of the fundamental frequency, spanning 12.7 optical octaves throughout the entire terahertz-to-visible domain between 0.1 and 675 THz. Our experiments establish a new field of light-wave electronics exploring coherent charge transport at optical clock rates and bring picosecond-scale electric circuitry at the interface of THz optics and electronics into reach.