Ice shelves are thick, floating ice masses most often associated with Antarctica where they are seaward extensions of the grounded Antarctic ice sheet and sources of many icebergs. However, there are also ice shelves in the Arctic, primarily located along the north coast of Ellesmere Island in the Canadian High Arctic. The only ice shelves in North America and the most extensive in the north polar region, the Ellesmere ice shelves originate from glaciers and from sea ice and are the source of ice islands, the tabular icebergs of the Arctic Ocean. The present state of knowledge and understanding of these ice features is summarized in this paper. It includes historical background to the discovery and early study of ice shelves and ice islands, including the use of ice islands as floating laboratories for polar geophysical research. Growth mechanisms and age, the former extent and the twentieth century disintegration of the Ellesmere ice shelves, and the processes and mechanisms of ice island calving are summarized. Surface features, thickness, thermal regime, and the size, shape, and numbers of ice islands are discussed. The structural-stratigraphic variability of ice islands and ice shelves and the complex nature of their growth and development are described. Large-scale and small-scale dynamics of ice islands are described, and the results of modeling their drift and recurrence intervals are presented. The conclusion identifies some unanswered questions and future research opportunities and needs.