Classical deterministic time evolutions exist with apparent random features, as is seen in hydrodynamic turbulence. Such phenomena have been called deterministic chaos, and are associated with sensitive dependence on initial conditions.
We discuss chaos theory with emphasis on the multidisciplinary work concerning chaos in natural phenomena during the three decades 1970-2000. Work in that period has involved developments in pure mathematics, new experimental techniques, and the use of digital computers. The problems addressed include hydrodynamical turbulence, meteorology, chemical kinetics, and the astronomy of the solar system. These problems can be handled with precision. More general applications of deterministic chaos theory remain open.