A review of the results of observing the effects of the most interesting ionospheric and magnetic storms that took place in 2018–2019 is presented. Ionospheric and magnetic storms are considered as components of geocosmic storms. In accordance with the systemic paradigm of L.F. Chernogor, a geocosmic storm is a complex of processes caused by a solar storm, reduced to synergistically interacting storms in a magnetic field (magnetic storm), ionosphere (ionospheric storm), atmosphere (atmospheric storm) and electric field atmospheric-ionospheric-magnetospheric origin (electric storm). Using the analysis of specific magnetic and ionospheric storms as an example, it is shown that, in addition to general patterns, each storm has its own individual characteristics. The expediency of a comprehensive study of the manifestations of each new geocosmic storm has been confirmed. A wide variety of ionospheric and magnetic storms have been confirmed. A weak magnetic storm is not necessarily accompanied by a weak ionospheric storm, while a strong one is accompanied by a strong one. An ionospheric storm can be single-phase (positive or negative) or multi-phase, when the phases alternate. Storms can last from several hours to many days. Storms are accompanied by both aperiodic and quasi-periodic variations. The latter are caused by atmospheric gravity waves (periods 10–180 min) and infrasound (period less than 5 min). Of all the components of a geocosmic storm, except for academic ones, ionospheric storms are of the greatest practical interest. It is these storms that limit the potential characteristics of radio systems for various purposes (telecommunications, radio navigation, radar, remote radio sounding, radio astronomy). It is shown that ionospheric storms are accompanied by the appearance of multipath, broadening of the Doppler spectra (and even their collapse), significant aperiodic and quasi-periodic variations in the Doppler frequency shift, the amplitude of radio signals, and the trajectories of radio waves in the decameter range. In particular, the height of reflection of radio waves changed during ionospheric storms by 50–180 km. The electron concentration during moderate negative ionospheric storms decreased up to 2 times, and during moderate positive ionospheric storms it increased up to 3 times. Under the action of atmospheric gravity waves, the relative amplitude of quasi-periodic variations in the electron concentration reached 50%, and due to low-frequency infrasound, it did not exceed 0.7%.