Recent developments in computational and theoretical studies of alpha-particle-driven Alfvén turbulence in both the long (k⊥ρi ≪ 1) and the short (k⊥ρi ≤ 1) wavelength regimes are reported. In the long wavelength regime, a hybrid particle-fluid model is solved numerically as well as analytically in a simple slab geometry. The dominant nonlinear interactions are found to be couplings between two Alfvén waves to generate a zero-frequency electromagnetic convective cell and strong E × B convection of resonant alpha particles, which result in significant changes in plasma equilibria. The fluctuation energies first increase, then saturate and decay. The alpha-particle transport is convective and significant but does not necessarily lead to an appreciable alpha-particle loss. A mode-coupling theory is developed to explain the simulation results. In the short wavelength regime, a reduced turbulence model that describes the coupled nonlinear evolutions of fluctuation spectrum and alpha-particle density profile nα(r,t) in the presence of an alpha-particle source Sα(r, t) is solved numerically. A steady state is achieved. The nonlinear saturation is due to ion Compton scattering-induced energy transfer to higher wave numbers. Alpha-particle transport is significant, and a diffusion coefficient of Dα ≃ 0.5 m2/s for International Thermonuclear Experimental Reactor (ITER)-like parameters is obtained. The effect of anomalous alpha-particle diffusion on alpha-particle power coupling to bulk plasmas is also discussed.