Coherent large-scale circulations (semi-organized structures) in turbulent convection were studied theoretically and experimentally in an air flow. Particle Image Velocimetry was used to determine the turbulent and mean velocity fields, and a specially designed temperature probe with twelve sensitive thermocouples was employed to measure the temperature field. The hysteresis phenomenon in turbulent convection was found by varying the temperature difference between the bottom and upper walls of the chamber. The hysteresis loop comprises the one-cell and two-cells flow patterns while the aspect ratio is kept constant. A new mean-field theory of turbulent convection is developed. In a shear-free turbulent convection the theory predicts the convective wind instability which causes formation of large-scale semi-organized fluid motions in the form of cells. The developed theory of semi-organized structures in turbulent convection is in agreement with the experimental observations. The observed coherent structures are superimposed on a small-scale turbulent convection. Thermal structure inside the large-scale circulations is neither homogeneous nor isotropic. The warm thermal plumes accumulate at one side of the large-scale circulation, and cold plumes accumulate at the opposite side of the large-scale circulation. The redistribution of the heat flux plays a crucial role in the formation of coherent large-scale circulations in turbulent convection. Predictions of the developed theory are also in a good agreement with the observed semi-organized structures in the atmospheric turbulent convection.