The emerging "bottom-up" nanotechnology reveals a new field of bioinspired nanomaterials composed of chemically synthesized biomolecules. They are formed from elementary constituents in supramolecular structures by the use of a developed nature self-assembly mechanism. The focus of this perspective paper is on intrinsic fundamental physical properties of bioinspired peptide nanostructures and their small building units linked by weak noncovalent bonds. The observed exceptional optical properties indicate a phenomenon of quantum confinement in these supramolecular structures, which originates from nanoscale size of their elementary building blocks. The dimensionality of the confinement gives insight into intrinsic packing of peptide supramolecular nanomaterials. QC regions, revealed in bioinspired nanostructures, were found by us in amyloid fibrils formed from insulin protein. We describe ferroelectric and related properties found at the nanoscale based on original crystalline asymmetry of the nanoscale building blocks, packing these structures. In this context, we reveal a classic solid state physics phenomenon such as reconstructive phase transition observed in bioorganic peptide nanotubes. This irreversible phase transformation leads to drastic reshaping of their quantum structure from quantum dots to quantum wells, which is followed by variation of their space group symmetry from asymmetric to symmetric. We show that the supramolecular origin of these bioinspired nanomaterials provides them a unique chance to be disassembled into elementary building block peptide nanodots of 1-2 nm size possessing unique electronic, optical and ferroelectric properties. These multifunctional nanounits could lead to a new future step in nanotechnology and nanoscale advanced devices in the fields of nanophotonics, nanobiomedicine, nanobiopiezotronics, etc.