We discuss the observation and theory of nonlinear wave interactions in astrophysical and space plasmas. Observational evidence of nonlinear mode-mode coupling in solar type III radio bursts, auroral whistler-mode radiation and active experiments in space is reviewed. The transition from order to chaos in nonlinear plasma wave interactions is analysed. For Hamiltonian four-wave interactions, the nonlinear dynamical process may undergo a chaotic transition via the quasi-periodicity route. For dissipative three-wave interactions, the nonlinear system may evolve from order to chaos via two different routes: period doubling and intermittency. It is shown that chaos in dissipative nonlinear three-wave coupling can be controlled by applying a small sinusoidal wave to the system.