Heterogeneous radical processes on ice surfaces play a vital role in the formation of building blocks of the biologically relevant molecules in space. Therefore, quantitative mechanistic details of the radical binding and radical reactions on ices are crucial in rationalizing the chemical evolution in the Universe. The radical chemistry on ice surfaces was explored at low temperatures by combining quantum chemical calculations and laboratory experiments. A range of binding energies was observed for OH, HCO, CH₃, and CH₃O radicals binding on ices. Computed reaction paths of the radical reactions on ices, OCS + H and PH₃ + D, explained the experimentally observed products. In both radical reactions, quantum tunnelling plays a key role in achieving the reactions at low temperatures. Our findings give quantitative insights into radical chemistry on ice surfaces in interstellar space and the planetary atmospheres.