The climate during the last glacial-interglacial cycle exhibits distinct climate states and variability in various time scales with different spatial characteristics. These changes occur for natural reasons, but their mechanisms are not well understood. Compared to the research on present-day climate, which involves influences of human activity, the investigation of the climate during the last glacial-interglacial cycle can attribute to discover the underlying process of natural climate change, and assistant us to have a better prediction of future climate. Additionally, in comparison to studies on proxies, climate models provide a simplified numerical representation of dynamical and thermodynamical processes governing different components of the Earth’s climate system, which is not able to be recorded in proxy data. In this dissertation work, our first scientific focus is to clarify the mechanistic effects of a higher Northern Hemisphere ice sheet on large-scale North Atlantic Ocean surface circulation and Atlantic Meridional Overturning Circulation (AMOC) during glacial climate periods. We use the Community Earth System Models (COSMOS) to simulate five representative climate states during the last glacial-interglacial cycle: the Eemian interglacial, Mid Holocene, Pre-industrial (PI), stadial Marine Isotope Stage3 (MIS3), presented by 32 kilo years before present (ka B.P.), and Last Glacial Maximum (LGM). We have examined mean climatological states and variability of major large-scale North Atlantic Ocean surface circulation elements, including the Subtropical Gyre (STG), Subpolar Gyre (SPG), and Gulf Stream. Our results show that the existing Laurentide Ice Sheet and the elevated Greenland Ice Sheet induce increased surface winds over the North Atlantic Ocean during the LGM and MIS3, which subsequently enhance the North Atlantic gyres and the Gulf Stream. In addition, statistical analysis suggests that the correlation between AMOC and surface winds is increased during glacial climate states. The second part of our work is targeted at the explanation of the difference of abrupt decadal climate changes during the last glacial-interglacial cycle. As documented in Greenland ice cores, abrupt decadal climate changes are less pronounced during maximum glacial conditions and strongly suppressed during the Holocene. We conduct hosing experiments for three different climate states during the last glacial-interglacial cycle (PI, 32 ka B.P. and the LGM). Our results show that the freshening of the surface North Atlantic Ocean leads to a similar reduction of the AMOC due to the freshwater perturbation, independent of the background climate. However, the subsequent recovery stages show distinct tempo-spatial characteristics, with respect to the initial AMOC resumption and the strength of a superposed AMOC overshoot. During the initial AMOC resumption, a stronger temperature inversion between the surface and intermediate layer (200-800 m) in the South Labrador Sea induces a quicker restart of convective processes (32ka B.P. > LGM > PI). A few decades later, an AMOC overshoot is caused by the advection of warmer and saltier tropical Atlantic Ocean water into the South Labrador Sea. In case of a glacial climate background, this provides a strong positive feedback on the initial resumption. In comparison to the 32ka B.P. experiment, this feedback is noticeably weaker during the LGM, and completely absent during the PI. Furthermore, the temporal isolation of South Labrador Sea and Greenland-Iceland-Norwegian Sea contributions to the AMOC overshoot highlights the combined role of the tropical Atlantic Ocean and the South Labrador Sea response to the overshoot dynamics. The dependence of the AMOC overshoot and the associated climatic response on the climate state provides a coherent concept in agreement with pronounced rapid climate changes during glacial times, as recorded by proxy data. In addition to use fully coupled atmosphere-ocean model for the studies of different mechanistic processes in the Earth’s climate system, we employ a regional high-resolution ocean model (the North Atlantic/Arctic Ocean-Sea Ice Model) for further understanding of the hydrographic process of the surface Nordic Seas during the LGM, which has been reconstructed to be in different conditions by proxies in the CLIMAP (the Climate Long-Range Investigation, Mapping and Prediction) and GLAMAP (the Glacial Atlantic Ocean Mapping) projects. Using the atmospheric forcing corresponding to the CLIMAP and GLAMAP indicated surface ocean, our experiments successfully rediscovered the sea surface temperatures (SSTs) and sea ice cover, in agreement with the proxy reconstructions. Furthermore, the internal dynamics in our LGM experiments provide an intermediate cooling conditions in the Nordic Seas, colder than the GLAMAP reconstruction, but warmer than the CLIMAP reconstruction during the LGM. Furthermore, both the GLAMAP and CLIMAP atmospheric forcing lead to similar directions and magnitudes of surface ocean circulation in the Nordic Seas during the LGM, in spite of distinct features of the SSTs and sea ice cover.