Driving nanomagnets by spin-polarized currents offers exciting prospects in magnetoelectronics, but the response of the magnets to such currents remains poorly understood. For a single domain ferromagnet, I will show that an averaged equation describing the diffusion of energy on a graph captures the low-damping dynamics of these systems. Specifically, I obtain analytical expressions for the critical spin-polarized currents needed to induce stable precessional states and magnetization switching in the zero temperature system as well as for the mean times of thermally assisted magnetization reversals in the finite temperature system, giving explicit expressions for the effective energy barriers conjectured to exist. I will then outline the problem of extending the analysis to spatially non-unifrom magnets, modeled by an infinite dimensional Hamiltonian system.