High-frequency quadrupole focusing (HFQF) has revolutionized ion linear accelerator technology. A brief historical essay on HFQF development is presented. Solutions to the prob„lems undertaken at the Institute for High Energy Physics (IHEP) during the design work and fabrication of linear accelerators with HFQF are discussed. Spatially homogeneous quadrupole focusing (SHQF or, in Western terminology, RFQ) is now used in the front ends of almost all ion linear accelerators. A linear accelerator with spatially periodic quadrupole focusing (SPQF or, in Western terminology, RFQ DTL) is successfully operating as part of the IHEP accelerator complex. Spatially periodic quadrupole focusing has a number of advantages, both for proton acceleration and in heavy ion linear accelerators.