The determination of damping mechanisms is one of the most fundamental problems of magnetism. It represents the elimination of the magnetic energy and thus has broad impact in both science and technology. The dynamic time scale in spintronic devices is controlled by the damping and the consumed power depends on the damping constant squared. In recent years, the interest in high perpendicular anisotropy materials and thin film structures have increased considerably, owing to their stability over a wide temperature range when scaling devices to nanometer length scales. However, the conventional measurement method-Ferromagnetic resonance (FMR) can not produce accurate damping results in the high magnetic crystalline anisotropy materials/structures, and the intrinsic damping reported experimentally diverges among investigators, probably due to the varying fabrication techniques. This thesis describes the application of the Kambersky torque correlation technique, within the tight binding method, to multiple materials with high perpendicular magnetic anisotropy ($\sim10^7$ erg/cm$^3$), in both bulk and thin film structures. The impact of the inevitable experimental defects on the energy dissipation is identified and the experimental damping divergence among investigators due to the material degree of order is explained. It is demonstrated that this corresponds to an enhanced DOS at the Fermi level, owing to the rounding of the DOS with loss of long-range order. The consistency of the predicted damping constant with experimental measurement is demonstrated and the interface contribution to the energy damping constant in potential superlattices and heterostructures for spintronic devices is explored. An optimized structure will be a tradeoff involving both anisotropy and damping. The damping related spin dynamics in spintronic devices for different applications is investigated. One device is current perpendicular to planes(CPP) spin valve. Incoherent scattering matrices are applied to calculate the angle dependent magnetoresistantce and obtain analytic expressions for the spin valve. The non-linearity of magnetoresistance can be quantitatively explained by reflected electrons using only experimental spin polarization as input. The other device is a spin-transfer-torque nano-oscillator. The Landau-Lifshitz-Gilbert equation is applied and the synchronization requirement for experimentally fabricated non-identical multi spintronic oscillators is explored. Power enhancement and noise decrease for the synchronized state is demonstrated in a temperature range. Through introducing combined electric and magnetic coupling effect, a design for an optimized feasible nanopillar structure suitable for thin-film deposition is developed.