1Introduction12Linear Random Waves. Some Basic Results93Exactly Solvable Models394Direct Perturbation Methods675From Inverse Scattering to Perturbative Approach916Dynamical Solitons under Random Perturbations1057Sine-Gordon Kinks under Random Perturbations1218Random Wave Packets in Nonlinear Media1459Dynamics of Randomly Modulated Solitons16910Waves in Nonlinear Stationary Inhomogeneous Media19711Numerical Study of the Single-Particle Motion21312Numerical Studies: A Panoramic View23113Nonlinear Klein-Gordon Models24314Simulations with Dynamical and Envelope Solitons261Conclusion273Bibliography275