This work reviews several properties of liquid water, including the dielectric constant and the proton-spin lattice relaxation, and draws attention to a bilinear behaviour defining a crossover in the temperature range 50 +/- 10 degrees C between two possible states in liquid water. The existence of these two states in liquid water plays an important role in nanometric and biological systems. For example, the optical properties of metallic (gold and silver) nanoparticles dispersed in water, used as nanoprobes, and the emission properties of CdTe quantum dots (QDs), used for fluorescence bioimaging and tumour targeting, show a singular behaviour in this temperature range. In addition, the structural changes in liquid water may be associated with the behaviour of biological macromolecules in aqueous solutions and in particular with protein denaturation.