The present state of weak and strong plasma turbulence and plasma heating by waves are reviewed, with emphasis on the exact solutions of the wave kinetic equations, such as the power-law Kolmogorov spectra and streamers in k→-space. The strong plasma turbulence generated by the modulational instability of linearly excited waves and their collapse is represented by strong Langmuir turbulence. Because of stabilizing Landau damping effects on the weak plasma instabilities most of the excited waves interact only with suprathermal particles and generate the suprathermal tails of the particle velocity distribution. This happens also in the process of collisionless energy transfer from one species of plasma to another, and plays an important role in the interaction of plasmas in planetary magnetospheres and comets. This is reviewed here.