With the appearance of superpower laser sources of relativistic/ultrarelativistic intensities in the last decade, the laser-QED-vacuum-matter interaction physics has entered a new phase that makes real the observation of many nonlinear quantum electrodynamic (QED) and classical-quantummechanical phenomena revealed more than fore-five decades ago, serious advance in new generation of laser-plasma accelerators of ultrahigh energies, nuclear fusion etc. Hence, the present review article will help explorers-experimentalists in this field to attract attention on the fundamental properties and peculiarities of the dynamics of induced free-free transitions at high and superhigh intensities of stimulated radiation fields. In this connection it is of special interest the induced Cherenkov, Compton, undulator/wiggler coherent processes, as well as cyclotron resonance in a medium -possessing with nonlinear resonances of threshold nature and leading to many important nonlinear effects or applications, which are considered in this review. Contents I. Introduction II. Induced Cherenkov Process with Strong Laser Fields A. Critical Intensity in the Induced Cherenkov Process. Nonlinear Threshold Phenomenon of Particle "Reflection" and Capture B. Laser Acceleration in Gaseous Media. Cherenkov Accelerator C. Cyclotron Resonance in a Medium. Nonlinear Threshold Phenomenon of "Electron Hysteresis" D. Coherent Radiation of Charged Particles in Capture Regime. Cherenkov Amplifier30 III. Quantum Effects in Induced Cherenkov Process A. Quantum Description of "Reflection" Phenomenon. Particle Beam Quantum Modulation at X-Ray Frequencies B. Spin Effects in Induced Cherenkov Process C. Reflection of Electron From the Phase Lattice of Slowed EM Wave D. Quantum Description of Capture Phenomenon in Induced Cherenkov Process E. Quantum Modulation of Charged Particles at Optical Harmonics IV. Vacuum Versions of "Reflection" and Capture Phenomenon A. Induced Nonlinear Compton Process B. Induced Nonlinear Undulator/Wiggler Process C. Inelastic Diffraction of Electron on a Traveling EM Wave D. Diffraction Regime of Electron Coherent Scattering on the Traveling Wave Phase-Lattice E. Bragg Regime of Electron Coherent Scattering on the Traveling Wave