Scientific observations of sea ice began more than a century ago, but detailed sea-ice models appeared only in the latter half of the last century. The high albedo of sea ice is critical for the Earth’s heat balance, and ice motion across the ocean’s surface transports fresh water and salt. The basic components in a complete sea-ice model must include vertical thermodynamics and horizontal dynamics, including a constitutive relation for the ice, advection and deformational processes. This overview surveys topics in sea-ice modeling from the global climate modeling perspective, emphasizing work that significantly advanced the state of the art and highlighting promising new developments.