Polar ice sheets play a fundamental role in Earth's climate system, by interacting actively and passively with the environment. Active interactions include the creeping flow of ice and its effects on polar geomorphology, global sea level, ocean and atmospheric circulation, and so on. Passive interactions are mainly established by the formation of climate records within the ice, in form of air bubbles, dust particles, salt microinclusions and other derivatives of airborne impurities buried by recurrent snowfalls. For a half-century scientists have been drilling deep ice cores in Antarctica and Greenland for studying such records, which can go back to around a million years. Experience shows, however, that the ice-sheet flow generally disrupts the stratigraphy of the bottom part of deep ice cores, destroying the integrity of the oldest records. For all these reasons glaciologists have been studying the microstructure of polar ice cores for decades, in order to understand the genesis and fate of ice-core climate records, as well as to learn more about the physical properties of polar ice, aiming at better climate-record interpretations and ever more precise models of ice-sheet dynamics. In this Part I we review the main difficulties and advances in deep ice core drilling in Antarctica and Greenland, together with the major contributions of deep ice coring to the research on natural ice microstructures. In particular, we discuss in detail the microstructural findings from Camp Century, Byrd, Dye 3, GRIP, GISP2, NorthGRIP, Vostok, Dome C, EDML, and Dome Fuji, besides commenting also on the earlier results of some pioneering ventures, like the Jungfraujoch Expedition and the Norwegian–British–Swedish Antarctic Expedition, among others. In the companion Part II of this work ( Faria et al., 2014), the review proceeds with a survey of the state-of-the-art understanding of natural ice microstructures and some exciting prospects in this field of research.