Since it has the potential to significantly reduce gaseous emissions in the near future, electrolytic hydrogen production using electricity generated from renewable energy sources, such as solar radiation, is key. Water splitting processes occurring in electrolyzer cells are complex phenomena. Therefore, to fully realize such processes, different technologies have been accounted for. The focus of this work is on the mathematical modeling of three different electrolyzer cells related technologies, (i) alkaline, (ii) proton exchange membrane (PEM), and (iii) decoupled water splitting. Accordingly, several existing mathematical models for alkaline and PEM electrolyzers are initially revised. Next, a comprehensive mathematical model capable of properly predicting the performance of the three electrolyzer technologies accounted for here is proposed. The developed mathematical models are then used to predict the behavior of electrolyzer cells under different operation conditions. The obtained results are finally compared in terms of cell voltages, cell efficiencies, and hydrogen production rates. When compared to other results available in the literature, the cell voltage ones obtained using the new proposed model are in relatively good agreement. Specifically, for a current density range of 0–200 mA/cm2, cell pressures between 10 and 40 bar, and a cell temperature of 60 °C, cell voltage requirements are between 1.25 and 1.75 V, with the E-TAC technology performing better than the other two ones accounted for. In addition, for current densities of more than 100 mA/cm2 and cell pressures below 5 bar, Faraday's efficiencies are almost the same for all three technologies, i.e., about 95%. However, for higher cell pressures, significant differences in Faraday's efficiency appear. Based on the work carried out, it is concluded that developing a sound mathematical model is crucial both for the comprehension of coupled and decoupled water electrolysis-related processes and for their use in the simplest and most reliable way.