Polar sea ice is a composite material structured on length scales ranging over many orders of magnitude. A principal challenge in modeling sea ice is how to use microstructural data to find effective or homogenized behavior relevant to large-scale geophysical and ecological models. Similar challenges arise in the analysis and design of complex materials used in various scientific, engineering and medical applications. From tiny brine inclusions to ice pack dynamics on oceanic scales, and from microbes to polar bears, we'll tour recent advances in multiscale modeling of sea ice, its ecosystems, and related composite media. Percolation theory, random matrices, Anderson localization, fractal geometry, computational topology, dynamical systems, and even twisted bilayer graphene will be encountered along the way. We’ll conclude by briefly describing a recent Arctic Mathpedition that brought math students to Alaska to study sea ice physics and biology.