This paper reviews the problems and successes of computing turbulent flow. Most of the flow phenomena that are important to modern technology involve turbulence. The review is concerned with methods for turbulent flow computer predictions and their applications, and describes several of them. These computational methods are aimed at simulating either as much detail of the turbulent motion as possible by current computer power or, more commonly, its overall effect on the mean-flow behaviour. The methods are still being developed and some of the most recent concepts involved are discussed.