This study continues previous publications devoted to kinetic processes in nonequilibrium hydrogen plasma. This review contains an analysis of the kinetics of hydrogen molecules in the ground state and in excited singlet electron states in various gas discharges. The distribution functions measured over the vibrational levels of a hydrogen molecule in the ground electron state are compared with those calculated within the developed level semiempirical collisional-radiative model of low-temperature hydrogen plasma. A database of the measured and calculated collisional-radiative characteristics of kinetic processes involving excited hydrogen molecules and the parameters of low-temperature hydrogen plasma is formed.