Why plasma harmonics?

We discuss the emergence of interest in the high-order harmonic generation (HHG) of ultrashort pulses propagated through laser-produced plasmas. It is shown that, during the last few years, substantial amendments of plasma HHG allowed in some cases the characteristics of gas HHG to be surpassed. The attractiveness of a new approach in coherent extreme ultraviolet radiation generation is demonstrated, which can also be used as a tool for laser-ablation-induced HHG spectroscopy of a giant class of solids. We present general ideas and prospects for this relatively new field of nonlinear optics.