Spin-wave instabilities driven by microwave fields display autooscillations, intermrttency, quasiperiodicity, perrod-doubling and chaos like other nonlinear dynamic systems. Several of these phenomena, first observed nearly 30 year ago, only recently have been investigated systematically and understood in the light of modern nonlinear dynamics. We review recent experimental results in yttrium- iron-garnet subject to three drfferent sprn-wave pumping mechanisms: parallel pumping, subsidiary resonance (first-order Suhl process) and premature saturatron of the main resonance (second-order Suhl process). A theoretical model derived from first principles leading to coupled nonlinear spin-wave equations is used to interpret the observed sprn-wave instabilities, auto-oscillations, and chaotic dynamics. lmprovements needed in the model are also indicated. © 1990 IEEE