An overview of researches is presented, which was focused on application of a theoretical hypothesis on the turbulent vortex dynamo to the study of tropical cyclogenesis. The dynamo effect is related to the special properties of small-scale helical turbulence with the broken mirror symmetry and was hypothesized to result in large-scale vortices generation in both hydrodynamic and atmospheric turbulence. To introduce this abstract theory into tropical cyclone research, a recent discovery of vortical moist convection in the tropics is emphasized. Based on this finding, we discuss and substantiate the crucial role of rotating cumulonimbus clouds, known as vortical hot towers (VHTs), as a necessary element to provide the dynamo effect. An analogy is traced between the role of interaction “moist convection—vertical wind shear” in creating the vortex dynamo in the atmosphere and the role of the mean electromotive force providing the MHD dynamo in electrically conducting medium. Throughout the review of novel results, a pivotal role of the Russian-American collaboration on examining a helical self-organization of moist convective atmospheric turbulence under tropical cyclone formation by use of cloud-resolving numerical simulation is accented. The efforts resulted in application of the vortex dynamo theory to diagnose a time when cyclogenesis commences in a favorable tropical environment. This may help elaborate a universally accepted definition of tropical cyclogenesis that currently does not exist and contribute to practical purposes of diagnosis and forecasting.