Magnetospheric accretion is a universal process occurring in magnetized astronomical objects, ranging from neutron stars and white dwarfs to young stars (YSOs) and planets. In the context of neutron stars, this process is linked with phenomena such as X-ray pulsars and ultra-luminous X-ray sources (ULXs). For YSOs, it results in ultraviolet (UV) excess and atomic emission lines. Understanding these dynamical processes is essential for interpreting observational data and sheds light on the impact of accretion on star/planet evolution. We have carried out first-principle three-dimensional magnetohydrodynamic (MHD) simulations to study magnetospheric accretion onto young stars. I will discuss physical insights gained from these simulations, which include filamentary accretion onto stars, asymmetric disk structures, variability in accretion (QPO), outflow structures, and the stellar spin evolution. In the second part of my talk, I will suggest that a new frontier for companion-disk interaction study is studying eccentric or/and inclined companions. I will then apply the newly developed theory to stars/BHs in AGN disks and suggest that Stars/BH-AGN disk interaction may be related to binary black hole formation and changing look AGN. Finally, I will combine above two parts of my talk and discuss how young planets (e.g. hot Jupiters) interact with the magnetospheric accretion, which reveals surprisingly rich dynamics for close-in planets.
