Electric double layers (DLs) related to surface effects, sheaths, and ambipolar fields in plasmas have been studied by Langmuir, Bohm, and others, however, only marginally and as a static phenomenon in some unique experiments. The study of electric fields inside plasmas was blocked by the otherwise very successful assumption of space-charge quasi-neutrality. Contrary to this, the existence of very high dynamic electric fields inside plasmas was established from the fact that very high laser intensities in plasmas exert nonlinear (ponderomotive) forces to accelerate electron and ion fluids by very large electric fields. For this case, a basically new two-fluid theory had to be developed for realistic plasmas with collisions and (non-linear) energy transfer. The resulting DLs (and inverted DLs) were computed and measured. The historical development of DLs shows that the dynamic electric field description may be a practical approach. The numerical output shows that all inhomogeneous plasmas possess internal electric fields oscillating with the local plasma frequency and damped by the collision frequency. These oscillations are driven by the whole dynamic development of the plasma motion, especially by the incident laser field (leading for the first time to a hydrodynamic model for coupling of the electromagnetic waves to Langmuir waves). The nonconservative field can be used to accelerate electrons to giga-electron-volt energies in the 1011 V/cm fields in cavitons produced with present-day lasers. Further conclusions involve E × B rotation of plasma in tokamaks and an E × B block acceleration of ions to giga-electron-volt energies. A new resonance at perpendicular incidence of the laser radiation on plasmas has been concluded, and the density-independent second harmonics emission may be explained by the analytical results achieved.