IceCube is a cubic-kilometer Cherenkov detector located in the deep ice at the geographic South Pole. The dominant event yield in the deep ice detector consists of penetrating atmospheric muons produced in cosmic ray air showers with energies above several 100 GeV. In addition, the surface array, IceTop, deployed above the IceCube deep ice detector, measures the electromagnetic signal and low-energy muons of the air shower. Hence, IceCube and IceTop yield unique opportunities to study cosmic rays with large statistics in great detail.

We discuss the latest results of air shower measurements from IceCube and IceTop, including the energy spectrum of cosmic rays from 250 TeV up to the EeV range. We will also report a measurement of the cosmic ray mass composition in the PeV to EeV range and show recent results from searches for PeV gamma ray sources in the Southern Hemisphere. In addition, results from a full-sky analysis of the cosmic ray anisotropy, using combined data from the IceCube and HAWC observatories, will be reported. Finally, we will present a measurement of the density of muons in the GeV range and discuss its consistency with predictions from hadronic interaction models.