The investigation of superintense laser-driven ion sources and their potential applications offers unique opportunities for multidisciplinary research. Plasma physics can be combined with materials and nuclear science, radiation detection and advanced laser technology, leading to novel research challenges of great fundamental and applicative interest. In this paper we present interesting and comprehensive results on nanostructured low density (near-critical) foam targets for TW and PW-class lasers, obtained in the framework of the European Research Council ENSURE project. Numerical simulations and experimental activities carried out at 100 s TW and PW-class laser facilities have shown that targets consisting of a solid foil coated with a nanostructured low-density (near-critical) foam can lead to an enhancement of the ion acceleration process. This stimulated a thorough numerical investigation of superintense laser-interaction with nanostructured near-critical plasmas. Thanks to a deep understanding of the foam growth process via the pulsed laser deposition technique and to the complementary capabilities of high-power impulse magnetron sputtering, advanced multi-layer targets based on near-critical films with carefully controlled properties (e.g. density gradients over few microns length scales) can now be manufactured, with applications outreaching the field of laser-driven ion acceleration. Additionally, comprehensive numerical and theoretical work has allowed the design of dedicated experiments and a realistic table-top apparatus for laser-driven materials irradiation, ion beam analysis and neutron generation, that exploit a double-layer target to reduce the requirements for the laser system.