In addition to observations and lab experiments, the scientific investigation of the Arctic and Antarctic sea ice is conducted through the employment of geophysical models. These models describe in a numerical framework the physical behavior of sea ice and its interactions with the atmosphere, ocean, and polar biogeochemical systems. Sea-ice models find application in the quantification of the past, present, and future sea-ice evolution, which becomes particularly relevant in the context of a warming climate system that causes the reduction of the Arctic sea ice cover. Because of the sea-ice decline, the navigation in the Arctic ocean increased substantially in the recent past, a trend that is expected to continue in the next decades and that requires the formulation of reliable sea-ice predictions at various timescales. Sea-ice predictions can be delivered by modern forecast systems that feature dynamical sea-ice models. The simulation of sea ice is at the center of this thesis: A coupled climate model with a simple sea-ice component is used to quantify potential impacts of a geoengineering approach termed "Arctic Ice Management"; the skill of current operational subseasonal-to-seasonal sea-ice forecasts, based on global models with a varying degree of sea-ice model complexity, is evaluated; and, lastly, an unstructured-grid ocean model is equipped with state-of-the-art sea-ice thermodynamics to study the impact of sea-ice model complexity on model performance. In chapter 2, I examine the potential of a geoengineering strategy to restore the Arctic sea ice and to mitigate the warming of the Arctic and global climate throughout the 21st century. The results, obtained with a fully coupled climate model, indicate that it is theoretically possible to delay the melting of the Arctic sea ice by ~60 years, but that this does not reduce global warming. In chapters 3 and 4, I assess the skill of global operational ensemble prediction systems in forecasting the evolution of the Arctic and Antarctic sea-ice edge position at subseasonal timescales. I find that some systems produce skillful forecasts more than 1.5 months ahead, but I also find evidence of substantial model biases and issues concerning data assimilation and model formulation. Chapter 5 deals with the impact of sea-ice model complexity on model performance. I present a new formulation of the FESOM2 sea-ice/ocean model with a revised description of the sea-ice thermodynamics, including various parameterizations of physical processes at the subgrid-scale. The model formulation grants substantial modularity in terms of sea-ice physics and resolution. The new system is used for assessing the impact of the sea-ice model complexity on the FESOM2 performance in different atmosphere-forced setups with a specific parameter-tuning approach and a special focus on sea-ice related variables. The results evidence that a more sophisticated model formulation is beneficial for the model representation of the sea-ice concentration and snow thickness, while less relevant for sea-ice thickness and drift. I also highlight a dependence of the model performance on the atmospheric forcing product used as boundary conditions. In the final part of this thesis, I formulate recommendations for future developments in the field of sea-ice modeling, with particular emphasis on FESOM2 and, more generally, on the modeling infrastructure under development at the Alfred Wegener Institute.