The geographic South Pole provides unique opportunities to study cosmic particles in the Southern Hemisphere. It represents an optimal location to deploy large-scale neutrino telescopes in the deep Antarctic ice, such as AMANDA or IceCube. In both cases, the presence of an array, constructed to observe extensive air showers, enables hybrid measurements of cosmic rays. While additional neutron monitors can provide information on solar cosmic rays, large detector arrays, like SPASE or IceTop, allow for precise measurements of cosmic rays with energies above several 100TeV. In coincidence with the signals recorded in the deep ice, which are mostly due to the high-energy muons produced in air showers, this hybrid detector setup provides important information about the nature of cosmic rays. In this review, we will discuss the historical motivation and developments towards measurements of cosmic rays at the geographic South Pole and highlight recent results reported by the IceCube Collaboration. We will emphasize the important contributions by Thomas K. Gaisser and his colleagues that ultimately led to the rich Antarctic research program which today provides crucial insights into cosmic-ray physics.