  The displacement of a single electron enables exciting avenues for
nanotechnology with vast application potential in quantum metrology, quantum
communication and quantum computation. Surface acoustic waves (SAW) have proven
itself as a surprisingly useful solution to perform this task over large
distance with outstanding precision and reliability. Over the last decade,
important milestones have been achieved bringing SAW-driven single-electron
transport from first proof-of-principle demonstrations to accurate,
highly-controlled implementations, such as coherent spin transport,
charge-to-photon conversion, or antibunching of charge states. Beyond the
well-established piezoelectric gallium-arsenide platform, first realisations of
acousto-electronic transport have also been carried out on the surface of
liquid helium. In this review article, we aim to keep track of this remarkable
progress by explaining these recent achievements from basic principles, with an
outlook on follow-up experiments and near-term applications.
