Spin-polarized current injected into a metallic ferromagnet can excite spin waves of very large amplitude. We use this unique property of spin current to study new types of magnetization dynamics in the strongly nonlinear regime. I will describe our recent measurements of spin-current-driven dynamics in nanomagnets and ferromagnetic nanowires. In these systems, we observe several unusual magneto-dynamic phenomena that include intrinsic spin wave self-localization, non-adiabatic stochastic resonance, rapid current-induced domain wall motion and size quantization of nonlinear magnon scattering. I will also discuss emerging technologies such as universal magnetic memory and microwave nanooscillators that utilize interactions between spin currents and magnetization.