This dissertation explores the interactions between spin-polarized currents and individual nanoscale magnets, focusing on the microwave-frequency magnetization dynamics these currents can excite. Our devices consist of two magnetic films (2-40 nm) separated by a nonmagnetic spacer (5-10 nm Cu or 1.25 nm MgO), patterned into a "nanopillar" of elliptical cross-section ~100 nm in diameter. One magnetic layer (a thicker or exchange-biased "fixed" layer) polarizes electron currents that then apply a spin transfer torque to the other "free" layer. We have developed several high-frequency techniques in which we excite magnetic dynamics with spin-polarized currents and detect the corresponding magnetoresistance oscillations R(t). By applying a direct current I, we can excite both small-angle and new types of large-angle spontaneous magnetic precession of the free layer, inducing a microwave voltage V(t) = IR(t) across the junction that we measure with a spectrum analyzer. By studying the linewidths of the corresponding spectral peaks as a function of bias and temperature, we find the oscillation coherence time (related to the inverse linewidth) is limited by thermal fluctuations: deflections along the precession trajectory for T < 100 K, and thermally-activated mode hopping for T > 100 K. We have also developed a new form of ferromagnetic resonance (FMR) in which we use microwave-frequency spin currents to excite dynamics, and a resonant (DC) mixing voltage to measure the response. With this technique we can directly probe the magnetic damping in both layers, identify the dynamical modes observed in the DC-driven experiment, observe phase locking with these modes, and even probe the physical form of the spin transfer torque. For metallic devices we find the torque is always confined to the plane of the layers? magnetizations, while for (MgO) tunnel junctions we find a new component of the torque perpendicular to this plane, appearing at higher bias voltages. This new FMR technique should be able to probe much smaller devices still, enabling new fundamental studies of even smaller magnetic samples, someday approaching the molecular limit.