This review article presents the results of radar studies of convective phenomena in Moldavia and the North Caucasus using Eulerian (ECS) and Lagrangian (LCS) coordinate systems. Application of the Lagrangian approach allowed us to exclude the influence of the tropospheric displacement and to obtain integral grid patterns of thunderstorm-hail processes. These structures are especially well manifested at small wind shears (up to 1 m/sec/km). At large shears, the mesh structures are transformed predominantly into linear structures. The methodology for obtaining integral pictures of radio echoes of thunderstorm processes is described. Intersections of linear elements, which we call faces, occur at nodes. The latter plays a particularly important role in the dynamics and kinematics of convective storms. The latter play a particularly important role in the dynamics and kinematics of convective storms. The development of storms occurs along the facets and at the nodes of meso-β-scale convective structures (MMCS), which explains the mechanisms of splitting and merging of storms: in the first case the facets diverge, in the second case they converge. The relations of motion vectors for different types of storms are obtained. It is shown that the direction of the radio echo canopy coincides with the storm motion trajectory; the evolution vector (propagation) for the most powerful storms deviates from the storm displacement direction by 80°–135°. The structure of the updated band within which the Flanking Line is formed for supercells and multicells is studied. Mnemonic rules have been derived that allow one to infer from instantaneous patterns of anvil orientation and the mutual location of storms whether they are converging or diverging, and to identify left- or right-moving storms. A hypothesis on the internal structure of the cold front of the 2nd kind is stated. The main conclusion of the work is that the evolution of storms is determined by the configuration of meso-β-scale convective structures. This explains various convective phenomena from unified positions. The results are applicable in works on modification of convective cloudiness, for ultra-short-term forecasts of dangerous phenomena, storm warnings of the population, rescue services, etc.