Researches into the problem of hyper-atom physics, a branch of atomic physics formed in recent decades as a result of study of highly excited hydrogen-like atoms with values of the principal quantum number of 10-1000, determining the size of the outer electron orbit, are reviewed. Efforts of a large research group were devoted to solution of this problem and to study of properties of hyper-atom medium both in space and in the Earth atmosphere. We describe a new found regularity of existence of strongly excited atoms at different medium parameters and present a new model of interaction between low-temperature plasma and neutral gas flows, which allowed one to explain some observed anomalous effects and relate them with specific critical phenomena in the field of interaction of these media. Wide prospects of hyper-atom technologies are demonstrated. The created wide-spectrum and wide-band generators are described; analogous quantum-electronic amplifiers are under development, and the possibility of creation of devices with high-temperature superconductivity is explored.