The structure of the atmosphere in regions of clear-air turbulence is investigated by means of aircraft observations of wind and temperature in combination with objective and subjective turbulence records. The nature of the aircraft data and the assumptions inherent in the analyses are described. The detailed fields of vertical and horizontal wind shear, stability and Richardson number are presented for turbulence encountered in three different patterns of flow, viz., a sharp trough, an anticyclonic jet stream, and an intense straight jet. Severe turbulence (equivalent in intensity to that measured by the same aircraft in a mature thunderstorm) was found in certain portions of the trough and ridge, and moderate turbulence existed in the straight jet. Comparison of these cases and of twenty other flights indicates certain similarities and certain differences of the flow conditions in the turbulent regions. The necessary and sufficient conditions for the existence of clear-air turbulence have not been isolated. However, certain mesoscale conditions that appear to be important include large vertical variations of both wind speed and direction, a discontinuity in lapse rate at an upper front or tropopause, sharp trajectory curvature, and appreciable vertical motions. These conditions are believed to favor the development of short, unstable waves that are probably the dominant turbulent mechanism.