Sea ice is a porous medium which covers, on average, 5 to 7 percent of the earth's oceans. To understand its role in geophysical and biological systems, one needs to know its physical, chemical and hydrological properties, and thus: its microstructure. The present monograph addresses the evolution of the sea ice microstructure and its salinity on the basis of the key parameter: the cellular spacin gat the interface between sea ice and seawater. After reviewing observations and earlier models, the problem is discussed on the basis of modern theories of pattern selection and convection. A novel approach to model the cell spacing selection problem is proposed. It is a macroscopic variant of the classical morphological stability theory, leading to confident predictions of the cellular spacing during unidirectional solidification of saline solutions. It is further demonstrated, how the theory may be consistently modified in the presence of natural solutal convection, the situation of sea ice floating on its own melt. The theoretical framework is then applied to analyse permeability and convective stability problems, relevant in the highly porous bottom fractions of natural sea ice. A combination of scalings derived from morphological stability theory, convective stability of the porous sea ice medium, and turbulent melt convection, is shown to lead to a realistic prediction of the stable salinity of sea ice during the growth season. The consistency of discussed theories and observations indicates the potential of using aqueous saline solutions, to improve the understanding of interfacial pattern and microstructure evolution during directional solidification.