David Keilin (Proc. Roy. Soc. Lond. B, 150, 1959, 149-191) coined the term 'cryptobiosis' (hidden life) and defined it as 'the state of an organism when it shows no visible signs of life and when its metabolic activity becomes hardly measurable, or comes reversibly to a standstill.' I consider selected aspects of the 300 year history of research on this unusual state of biological organization. Cryptobiosis is peculiar in the sense that organisms capable of achieving it exhibit characteristics that differ dramatically from those of living ones, yet they are not dead either, so one may propose that cryptobiosis is a unique state of biological organization. I focus chiefly on animal anhydrobiosis, achieved by the reversible loss of almost all the organism's water. The adaptive biochemical and biophysical mechanisms allowing this to take place involve the participation of large concentrations of polyhydroxy compounds, chiefly the disaccharides trehalose or sucrose. Stress (heat shock) proteins might also be involved, although the details are poorly understood and seem to be organism-specific. Whether the removal of molecular oxygen (anoxybiosis) results in the reversible cessation of metabolism in adapted organisms is considered, with the result being 'yes and no', depending on how one defines metabolism. Basic research on cryptobiosis has resulted in unpredicted applications that are of substantial benefit to the human condition and a few of these are described briefly.