The last glacial period was characterized by abrupt switches between cold and warm climate regimes recorded in Greenland ice cores. The proximity of Greenland to the sea ice edge, among other factors, suggests that sea ice played an important role in these climate changes. In modern times, recent decades have seen a rapid retreat of Arctic sea ice. This thesis investigates the physical processes governing these abrupt changes in North Atlantic climate. The questions are approached using global climate models, idealized models, and observational analysis. The main findings of this research are summarized as follows: (i) the atmospheric response to receding glacial ice sheets, with sea ice amplification, may have contributed to the Younger Dryas abrupt cold interval 12,000 years ago; (ii) glacial climate may allow multiple states supported by feedbacks between sea ice and ocean circulation, with Dansgaard-Oeschger abrupt warming cycles being jumps between them; (iii) the disparity between rates of annual maximum (March) and annual minimum (September) sea ice extent retreat during recent decades may be due to coastline geometry; (iv) due to the impact of cloud simulation errors on Arctic sea ice, global climate model simulations of present-day sea ice conditions may agree less well than previous studies have suggested; (v) the possibility of a "tipping point" as Arctic sea ice recedes may be unlikely in the near future but likely in a more distant approach to perennially ice-free Arctic Ocean conditions. This work has direct implications regarding the cause of abrupt climate changes during the last glacial period, the characteristics of modern observed sea ice retreat, and the prediction of future changes in Arctic sea ice conditions.