Resent research on high-order harmonic generation in laser-produced plasmas is reviewed. We analyze the conditions for the generation of harmonics (up to the 101st order, . ~ 7.9 nm) in the propagation of laser radiation through a weakly-ionized plasma prepared by irradiating the surfaces of different targets with a laser prepulse. First experiments on attosecond pulse generation from plasma plumes are presented. We discuss the findings of investigations into the resonance intensity enhancement of individual harmonics in a number of plasma formations, which have demonstrated a substantial increase in the conversion efficiency in the plateau region of the harmonic distribution (in particular, of the 13th harmonic in indium plasmas with the efficiency 10-4). We review the results of investigations of harmonic generation in nanoparticle-containing plasmas (metallic clusters, fullerenes, nanotubes). Different techniques for increasing the intensity and order of the generated harmonics are discussed. Future perspectives are analyzed as well. Among them are: (a) high-power harmonics from nanoclusters at 1 kHz pulse repetition rates, (b) few-cycle pump-induced harmonics, (c) molecular orientation in plasma plumes, (d) attosecond experiments, (e) plasma manipulations, (e) carbon-containing plasma: perspectives of application for plasma HHG, (f) long-wavelength femtosecond pump.
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