Hydrogen evolution reaction (HER) by splitting water is a key technology toward a clean energy society, where Pt-based catalysts were long known to have the highest activity under acidic electrochemical conditions but suffer from high cost and poor stability. Here, we overview the current status of Pt-catalyzed HER from a theoretical perspective, focusing on the methodology development of electrochemistry simulation, catalytic mechanism, and catalyst stability. Recent developments in theoretical methods for studying electrochemistry are introduced, elaborating on how they describe solid-liquid interface reactions under electrochemical potentials. The HER mechanism, the reaction kinetics, and the reaction sites on Pt are then summarized, which provides an atomic-level picture of Pt catalyst surface dynamics under reaction conditions. Finally, state-of-the-art experimental solutions to improve catalyst stability are also introduced, which illustrates the significance of fundamental understandings in the new catalyst design.