This paper reviews the progress in applying the plasma-driven solution electrolysis (PDSE), which is also referred to as the contact glow-discharge electrolysis (CGDE) or plasma electrolysis, for hydrogen production. The physicochemical processes responsible for the formation of PDSE and effects occurring at the discharge electrode in the cathodic and anodic regimes of the PDSE operation are described. The influence of the PDSE process parameters, especially the discharge polarity, magnitude of the applied voltage, type and concentration of the typical electrolytic solutions (K2CO3, Na2CO3, KOH, NaOH, H2SO4), presence of organic additives (CH3OH, C2H5OH, CH3COOH), temperature of the electrolytic solution, the active length and immersion depth of the discharge electrode into the electrolytic solution, on the energy efficiency (%), energy yield (g(H2)/kWh), and hydrogen production rate (g(H2)/h) is presented and discussed. This analysis showed that in the cathodic regime of PDSE, the hydrogen production rate is 33.3 times higher than that in the anodic regime of PDSE, whereas the Faradaic and energy efficiencies are 11 and 12.5 times greater, respectively, than that in the anodic one. It also revealed the energy yield of hydrogen production in the cathodic regime of PDSE in the methanol−water mixture, as the electrolytic solution is 3.9 times greater compared to that of the alkaline electrolysis, 4.1 times greater compared to the polymer electrolyte membrane electrolysis, 2.8 times greater compared to the solid oxide electrolysis, 1.75 times greater than that obtained in the microwave (2.45 GHz) plasma, and 5.8% greater compared to natural gas steam reforming.