The paper describes results of theoretical investigation of high-power laser beam propagation along the ground and high-altitude atmospheric paths as well as the potentialities of remote measurement of beam characteristics. The paper presents an overview of the algorithms for solving the problems of laser radiation blooming based on the method of statistical tests, the equation for statistical moments of a field complex amplitude and the radiation transfer equation. The parameters of partially coherent radiation along characteristic atmospheric paths are analyzed. Recommendations are given on how to optimize the radiation focusing and power. The theoretical grounds of new methods for diagnostics of spatial-power and phase characteristics of laser beams are presented. We also present some results of numerical and laboratory experiments on reconstruction of the intensity and phase distributions.