Two complementary effects modify the GHz magnetization dynamics of nanoscale hybrid structures of ferromagnetic and normal materials from those of the isolated magnetic constituents: On the one hand, a time-dependent ferromagnetic magnetization pumps a spin angular-momentum flow into adjacent materials and, on the other hand, spin angular momentum is transferred between ferromagnets by an applied bias that corresponds to mutual torques on the magnetizations. These phenomena are manifestly nonlocal: they are governed by the entire spin-coherent region that is limited in size by the spin-relaxation processes. We review recent progress in understanding the magnetization dynamics in ferromagnetic hybrid structures from first principles, focusing on the role of the spin pumping. The main body of the theory is semiclassical and based on a mean-field Stoner or spin-density-functional picture, but quantum-size effects and the role of electron-electron correlations are also discussed. A growing number of experiments support the theoretical predictions. The formalism should be useful to understand the physics and engineer the characteristics of small devices such as magnetic random-access memory elements.