Summary: We describe the development of mathematical models of ice sheets, focusing on underlying physics and the minimal components that successful models must contain. Our review describes the basic fluid dynamical ice-flow models currently in use; points out numerous poorly understood thermomechanical feedbacks in ice flow; and describes the current, often poorly constrained, state of models for ice-sheet sliding and subglacial drainage, as well as their role in ice-stream dynamics. We conclude with a survey of marine ice-sheet models, outlining recent developments of self-consistent free-boundary models and ongoing research into three-dimensional marine ice sheets.
For the entire collection see [Zbl 1258.76021].