Solar wind-magnetosphere-ionosphere (SW-M-I) coupling is investigated with three different computational models that characterize space plasma dynamics on distinct spatial/temporal scales. These models are used to explore three important aspects of SW-M-I coupling. A particle-in-cell (PIC) model has been developed to explore the kinetic scale dynamics associated with the magnetotail dipolarization front (DF), which is generated as a result of magnetotail reconnection. The PIC study demonstrates that the electron-ion hybrid (EIH) instability could relax the velocity shear within the DF via emitting lower hybrid waves. The velocity inhomogeneity driven instability is highlighted as an important mechanism for energy conversion and wave emission during the solar wind-magnetosphere coupling, which has been long neglected before. The Lyon-Fedder-Mobbary (LFM) global magnetohydrodynamic (MHD) model is used to explore the fluid scale electrodynamic response of the magnetosphere-ionosphere to the interplanetary electric field (IEF). It is found that the cross polar cap potential (CPCP) varies linearly with very large IEF if the solar wind density is high enough. With controlled experiments of global MHD modeling driven by observed parameters, the linearity was interpreted as a result of the magnetosheath force balance theory. This study highlights the role of solar wind density in the electrodynamic SW-M-I coupling under extreme driving conditions. The LFM-TIEGCM-RCM (LTR) model, which is the Coupled-Magnetosphere-Ionosphere-Thermosphere (CMIT) model with Ring Current extension, is used to explore the integrated SW-M-I system. The LTR simulation study focuses on the subauroral polarization streams (SAPS), which involve both MHD and non-MHD processes and three-way coupling in the SW-M-I system. The global structure and dynamic evolution of SAPS are illustrated with state-of-the-art first-principle models for the first time. This study has successfully utilized multiscale models to characterize the forefront issues in the space plasma dynamics, which is required by the facts that plasmas have both particle and fluid featured properties and those properties are vastly different across geospace regions. It is highlighted that SW-M-I coupling could be significantly influenced by both microscopic and macroscopic processes. In order for a comprehensive understanding of the SW-M-I coupling, multiscale models and integrated framework of their combinations are critical.