We research experimentally and theoretically freestanding (self-supported) nanomembranes with thickness below 100 nm (down to 3-4 nm). We fabricated metal composite freestanding structures with thickness below 8 nm and lateral dimensions of several millimeters. We also investigated various methods for functionalization of nanomembranes, including introduction of nanofillers, lamination and surface sculpting. Particularly we perform research of nanomembranes with plasmonic properties, supporting long-range plasmons polaritons and usable for chemical sensing.