The magnetic reconnection of magnetosphere and the magnetospheric space storms (including magnetospheric substorm, magnetic storm, magnetospheric particle storm) has long been one of the most challenging subjects in the solar-terrestrial physics. The reconnection mechanism and global triggering process of the magnetospheric space storms are still unclear up to now. Based on the Double Star Program (DSP) and Cluster joint measurements, we have observed the solar wind density hole, the component magnetic field reconnection in the magnetopause, the structures of magnetic storm ring current, global and multi-scale driven and triggering processes of magnetospheric substorm. In this paper we will briefly introduce these results. solar wind, magnetic reconnection, magnetospheric substorm, magnetic storm Magnetic reconnection at the magnetopause is the primary mechanism responsible for the transfer of solar wind energy into the magnetosphere. Previous observations have considerably increased the understanding of this key process in the solar wind-magnetosphere coupling. However, some fundamental questions remain unclear. It is not yet known which process dominates the dayside magnetic reconnection when a non-zero interplanetary magnetic field (IMF) B y is present, anti-parallel merging at high latitudes [1,2] , or component merging at low latitudes near the subsolar point [3,4] . Whether reconnection can operate in the dayside low-latitude magnetopause for northward IMF B z is also a matter of ongoing discussions. How the flux transfer events (namely, the open flux ropes) are formed and how their global pattern looks like those formed FTE are still unclear and of interest to the community of space science. Another challenging problem in space plasma research is the quest for the physical processes responsible for the onset of magnetospheric substorms that are generally considered to be akin to many phenomena related to the energetic storage and explosion observed throughout the plasma universe. There are many substorm onset