||We give a review of drilling to the beds of the Greenland and Antarctic ice sheets, with a history of just a century. We use a chronological rather than a geographical ordering to emphasize the way drilling has developed. The review is divided into two parts: core drilling and hole-only drilling for access to the beds or the deep interior of the ice sheets. This is an overview, not a comprehensive report on each project. While we have endeavoured to include all projects that fit our selection criteria, we have not provided all the technical details.