The dramatic decline of the summer Arctic ice pack is perhaps the most visible, large scale change on Earth's surface in recent years. Most global climate models, however, have underestimated this decline, while the Antarctic sea ice pack has increased. Fluid flow through porous sea ice mediates some key processes which must be better represented in climate models, such as snow-ice formation and the evolution of melt ponds and ice pack reflectance. We will describe recent advances in using percolation, network, and diffusion models to predict the fluid permeability of sea ice. We'll also discuss X-ray CT imaging of the brine microstructure and connectivity analysis of random graphs derived from the tomographic images. Our work will help in predicting how global warming may affect sea ice, and the response of polar ecosystems. Related results on electromagnetic properties will help in monitoring ice thickness. Video from a 2007 Antarctic expedition where we measured fluid and electrical transport in sea ice will be shown.