Our recent discovery of three new phases of ice has increased the total number of known distinct polymorphs of ice to fifteen. In this Perspective article, we give a brief account of previous work in the field, and discuss some of the particularly interesting open questions that have emerged from recent studies. These include (i) the effectiveness of acid and base dopants to enable hydrogen-ordering processes in the ices, (ii) the comparison of the calorimetric data of some of the crystalline phases of ice and low-density amorphous ice, (iii) the disagreement between the experimental ice XV structure and computational predictions, (iv) the incompleteness of some of the hydrogen order/disorder pairs and (v) the new frontiers at the high and negative pressure ends of the phase diagram.
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