Sea ice is a crucial component of polar climate systems, and is undergoing substantial changes in both the Arctic and the Southern Ocean due to evolving climatic conditions. The Arctic Ocean is undergoing a transition from being perennially ice-covered to be- ing only seasonally ice-covered. The shrinking and thinning of ice cover have been at- tributed to changes in atmospheric and oceanic forcing, as well as to changes in the phys- ical properties of pack ice. The Southern Ocean also shows signs of change, reflected in recent minima and amplified seasonality. As global warming persists in the coming decades, the role of sea ice in polar climate systems is poised for further transformation. How- ever, current theoretical frameworks and parameterization methods used in numerical models to simulate sea ice evolution and its interaction with the oceanic and atmospheric boundary layers are largely rooted in measurements from an earlier era characterized by thicker multiyear ice. In this review we aim to summarize the evolution of physical drivers governing the dynamics and thermodynamics of sea ice, snow, and ocean/atmosphere boundary layers. Furthermore, we describe and assess existing parameterization meth- ods of sub-grid scale processes, discuss recent observational findings, and propose essen- tial improvements.