||The subject of current induced magnetic reversal has received considerable interest recently due to its attractive property for magnetic nanodevice applications. In this thesis, 3D simulations are performed to study current induced magnetic domain motion in magnetic nanostrips and nanowires based on the Landau-Lifshitz-Gilbert model with a spin transfer torque. For sufficiently thin strips and wires, the LLG equation can be reduced to a one dimensional model. For the simplified models, the dynamic laws for the domain wall motion are derived from a matched asymptotic expansion. The results are consistent with the numerical results. We also study the current induced magnetic domain wall motion in magnetic nanostrips with defects. Our numerical results show that when a domain wall passes through a defect, it experiences a strong attracting force. There is a critical current density below which the domain wall will oscillate around the defect and eventually be pinned at the defect. From the asymptotic expansion analysis, we show that the amplitude of this domain wall oscillation can be resonantly amplified by an ac current with proper frequency for the first time. This suggests a way to reduce the critical current for depinning of the domain wall.