Heavy ion sources for the big accelerators, for example, the LHC, require considerably more ions per pulse during a short time than the best developed classical ion source, the electron cyclotron resonance (ECR) provides; thus an alternative ion source is needed. This can be expected from laser-produced plasmas, where dramatically new types of ion generation have been observed. Experiments with rather modest lasers have confirmed operation with one million pulses of 1 Hz, and 1011 C4+ ions per pulse reached 2 GeV/u in the Dubna synchrotron. We review here the complexities of laser-plasma interactions to underline the unique and extraordinary possibilities that the laser ion source offers. The complexities are elaborated with respect to keV and MeV ion generation, nonlinear (ponderomotive) forces, self-focusing, resonances and “hot” electrons, parametric instabilities, double-layer effects, and the few ps stochastic pulsation (stuttering). Recent experiments with the laser ion source have been analyzed to distinguish between the ps and ns interaction, and it was discovered that one mechanism of highly charged ion generation is the electron impact ionization (EII) mechanism, similar to the ECR, but with so much higher plasma densities that the required very large number of ions per pulse are produced.