Recent work on the dynamics of one-dimensional spin glasses with nearest-neighbor Heisenberg interactions is reviewed with particular emphasis on the linearized spin excitations or magnons. The distribution and the spatial extent of these modes is investigated using numerical modeling techniques and the results compared with various theoretical calculations. Studies are carried out in the zero-field and high-field limits. In the latter limit, an approximate theory based on a Coherent Exchange Approximation is shown to yield results near the spin precession frequency that are in good agreement with the simulation data.