The ultrafast (sub-nanosecond) magnetization dynamics of ferromagnetic thin films and elements that find application in spintronic devices is reviewed. The major advances in the understanding of magnetization dynamics in the two decades since the discovery of giant magnetoresistance and the prediction of spin-transfer torque are discussed, along with the plethora of new experimental techniques developed to make measurements on shorter length and time scales. Particular consideration is given to time-resolved measurements of the magneto-optical Kerr effect, and it is shown how a succession of studies performed with this technique has led to an improved understanding of the dynamics of nanoscale magnets. The dynamics can be surprisingly rich and complicated, with the latest studies of individual nanoscale elements showing that the dependence of the resonant mode spectrum upon the physical structure is still not well understood. Finally, the article surveys the prospects for development of high-frequency spintronic devices and highlights areas in which further study of fundamental properties will be required within the coming decade.