The buildup of the energetic particle population in fusion plasmas is typically slow compared to the growth times of energetic-particle driven instabilities. This feature draws special attention to nonlinear studies of unstable waves in the near-threshold regimes. The goal is to characterize the long-time behavior of the weakly dissipative waves and resonant particles in the presence of particle sources and sinks. There are numerous experimental observations of energetic-particle driven instabilities. In some cases the unstable modes grow to a level at which they cause enhanced transport and anomalous losses of the fast particles. In other cases the losses are small but the modes exhibit an intricate nonlinear behavior: generation of sidebands, quasi-periodic bursts, change of the mode frequency in time, etc. This lecture, presented at the 4th ITER International Summer School in Austin, Texas, provides a first-principles physics basis for understanding these phenomena.