The article reviews recent progress in understanding the magnetization dynamics in ferromagnetic heterostructures, focusing on the role of spin pumping and spin-flip relaxation. The authors discuss the nonlocal exchange coupling and giant magnetoresistance (GMR) in ferromagnetic multilayers, the Landau-Lifshitz-Gilbert (LLG) phenomenology for magnetization dynamics, and the current-induced magnetization dynamics. They also explore the spin emission by coherently precessing ferromagnets and the Gilbert damping enhancement. The formalism is derived from microscopic principles and is applicable to quasi-one-dimensional models, such as layered pillar structures. The review covers both theoretical developments and experimental confirmations, highlighting the importance of spin-orbit coupling and electron-electron interactions. The authors conclude by discussing the implications of these findings for the design of small devices like magnetic random-access memory elements.The article reviews recent progress in understanding the magnetization dynamics in ferromagnetic heterostructures, focusing on the role of spin pumping and spin-flip relaxation. The authors discuss the nonlocal exchange coupling and giant magnetoresistance (GMR) in ferromagnetic multilayers, the Landau-Lifshitz-Gilbert (LLG) phenomenology for magnetization dynamics, and the current-induced magnetization dynamics. They also explore the spin emission by coherently precessing ferromagnets and the Gilbert damping enhancement. The formalism is derived from microscopic principles and is applicable to quasi-one-dimensional models, such as layered pillar structures. The review covers both theoretical developments and experimental confirmations, highlighting the importance of spin-orbit coupling and electron-electron interactions. The authors conclude by discussing the implications of these findings for the design of small devices like magnetic random-access memory elements.