This paper is devoted to the investigation of powerful laser pulse interaction with regularly and statistically volume-structured media with near critical average density and properties of laser-produced plasma of such a media. The results of the latest experiments on laser pulse interaction with plane foam targets performed on Nd-laser facilities “ABC” in the ENEA-EURATOM Association (Frascati, Italy) and “MISHEN” in the Troitsk Institute of Innovation Thermonuclear Investigations (TRINITI, Troitsk Russia), and J-laser “ISKRA-4” in the Russian Federal Nuclear Center, All-Russian Scientific Research Institute of Experimental Physics (RFNC-VNIIEF, Sarov, Russia) are presented and analyzed. High efficiency of the internal volume absorption of laser radiation in the foams of supercritical density was observed, and the dynamics of absorbing region formation and velocity of energy transfer process versus the parameters of porous matter are found. Some inertial confinement fusion (ICF) applications based on nonequilibrium properties of laser-produced plasma of a foam and regularly structured media such as the powerful neutron source with yield of 109–1011 DT-neutrons per 1 J of laser energy, laser-produced X-ray generation in high temperature supercritical plasma, and the compact ICF target absorbers providing effective smoothing and ablation are proposed.