A comprehensive understanding of the origin of cosmic rays, as well as processes responsible for their acceleration to extreme energies and their propagation through the interstellar medium, requires precise measurements of their energy spectrum, mass composition, and anisotropy, from both space- and ground-based experiments, such as DAMPE, GRAPES-3 and IceCube, which are essential for validating and refining theoretical models. The GRAPES-3 experiment, located in Ooty, India, is dedicated to the measurement of cosmic-ray air showers over an energy range extending from a few TeV to several tens of PeV, with significant overlap with space-based observations and covering the knee region of the cosmic-ray spectrum. Additionally, the surface component of the IceCube Neutrino Observatory, situated at the South Pole, records cosmic-ray air showers in the primary energy range from PeV to EeV, and primarily investigates cosmic rays in the transition region from Galactic to extragalactic origin. The combined measurements from GRAPES-3 and IceCube offer a broad energy range to investigate the energy spectrum and mass composition or cosmic rays. In this talk, the first observation of spectrum hardening in the cosmic ray proton energy spectrum at around 165 TeV by the GRAPES-3 experiment will be presented. It will be followed by results from ongoing cosmic-ray analyses with GRAPES-3 and IceCube. These include separate measurements of the all-particle energy spectrum from GRAPES-3 and IceCube, studies of hadronic interaction models, and investigations of air-shower arrival direction reconstruction with IceCube.