Polar sea ice is a key component of Earth’s climate system. As a material it exhibits complex composite structure on length scales ranging from tenths of millimeters to tens of kilometers. A principal challenge in modeling sea ice and its role in climate is in relating behavior and structure on small scales to effective or homogenized behavior on larger scales, and in estimating parameters controlling small scale processes from large scale observations. In this lecture we address fundamental questions in sea ice homogenization, and the development of Stieltjes integral representations and rigorous bounds for effective parameters in the sea ice system. In particular, we consider fluid, thermal, and electromagnetic transport through sea ice, advection enhanced diffusion processes, and the propagation of ocean waves through the sea ice pack. This work is helping to advance how sea ice is represented in climate models, and to improve projections of the fate of Earth’s sea ice packs and the ecosystems they support.