In conjunction with the amplified Arctic warming and drastically retreating sea ice, extremely intense cyclones have been more frequently observed throughout the year in the Arctic. These cyclone systems have also, in turn, enhanced air-sea-ice interactions, leading to transient warming and sea ice loss events and cumulatively contributing to the long-term Arctic climate changes. We conduct systematic analysis of Arctic cyclone activity from its climatic variability and changes to process-level studies on selected rare extreme cases using both reanalysis datasets and model simulations. The results indicate that Arctic cyclone activity, measured by an energy-based, integrative index, has intensified during last seven decades, which is supported by the CMIP6 model historical simulations. The underlying physical mechanisms are increased surface baroclinicity due to sea ice retreat and warmed open ocean, as well as the strengthened downward influence of the stratospheric vortex. When examining specific intense cyclone cases, it is found that intense summer cyclone can induce Ekman upwelling, transporting subsurface warm water to the upper ocean, and increase upper ocean mixing. As a consequence, summer sea ice melt accelerates. During winter, intense cyclones can trigger blowing snow, moisten the atmospheric boundary layer, and form low level clouds, favoring surface warming and sustaining polynya. Further analysis also suggests that higher model spatial resolution captures more numerous cyclones, which is important for understanding the finer-scale interactive processes between cyclones and the underlying sea ice and ocean.