At a time of substantial Arctic sea-ice change, and with increasing attention by a range of different interests in the polar regions, it is helpful to review briefly our current understanding of key sea-ice processes and properties, as well as the methods employed in their study. This contribution focuses on those properties relevant in the context of recent reductions in the age and summer minimum extent of Arctic sea ice. Assessing and predicting the impacts of such changes requires a thorough understanding of the exact nature of the transformation, in particular its effects on properties of the ice that may be at the heart of feedback effects or are disproportionately important for polar ecosystems, regional and global climate, or human activities. Here, the most important variables include the thickness of the ice and snow cover and its distribution, as well as properties that control the transport of energy and matter through sea ice. The presentation will provide a brief review of the state of the art with respect to our understanding of these key properties and our ability to measure and track their evolution through space and time. Knowledge gaps will be highlighted and we will consider what might be required in the way of technological development to close such gaps. Finally, we will explore the challenges posed to sea-ice geophysics by other disciplines that require (in some cases urgent) answers to questions raised in response to recent Arctic change.