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. / Doctor of Philosophy / Three numerical models are used to explore the processes occurring in the Earth’s space environment from an altitude of ∼ 100 km to 10s Earth radii (R_E). This environment is mainly filled with plasma, the gaseous state of charged particles that collectively behave like a fluid and are also subject to complex electromagnetic interactions. The intrinsic features of plasma determine that the physics on the scale of charged particles and that on the scale of fluids are both very important. On the other hand, considering the vast differences in the plasma properties throughout space, different regions need to be represented by different physically-based models. This dissertation study addresses the processes on three distinct spatial/temporal scales with different models. A particle model that treats plasma as a group of charged particles is used to explore wave generation in the magnetotail (10s R_E in the nightside). It is found that inhomogeneous plasma flow in the sharp boundary layer at the magnetotail (called “dipolarization front”) can excite plasma waves to dissipate the energy originating from the solar wind (high speed plasma ejected from the sun). A magnetohydrodynamic (MHD) model that treats the plasma as a magnetized fluid is used to explore the efficiency of electric field mapping from the solar wind (10s R_E) to the ionosphere (∼ 100 km altitude). The electric field in the ionosphere usually linearly increases with solar wind electric field until it is too strong. An observational event showed that their relationship remains linear for very large driving field. MHD modeling experiments demonstrate that the linearity at large driving field is due to the high solar wind density, which is explained with force balance theory. An integrated model framework is used to explore the system level response of geospace by investigating the enhanced plasma flow in the subauroral ionosphere (called the subauroral polarization streams, SAPS). The generation of SAPS involves driving and feedback processes in different regions (magnetosphere, ring current, ionosphere) that can not be simulated with any individual model. The global structures and dynamic evolution of SAPS have never been explored before with first-principle characterization of the effects from the solar wind to geospace. This integrated modeling represents a state-of-the-art model framework to explore processes in coupled geospace. These studies illustrate that different models are necessary to explore fundamental physics on small and large scales and the coupling processes between different space regions. It is also suggested that incorporating the different models into an integrated framework is necessary to get a comprehensive understanding of the dynamics in geospace.