With the exponential rise in global energy demand, the depletion of fossil fuels, and the resulting environmental pollution, the development of renewable clean energy sources has become a critical priority. It is reported that due to population growth, global energy consumption will rise to ~40.8 TW in 2050. Therefore, the world needs to formulate sustainable energy sources that compete with fossil fuels in terms of efficiency and cost with zero carbon emission. Hydrogen technologies are crucial in tackling the energy crisis and mitigating environmental challenges. Water splitting through electrolysis stands out as one of the most promising methods for hydrogen production. However, its implementation requires the development of cost-effective and efficient hydrogen evolution reaction (HER) catalysts to replace the reliance on noble metal-based alternatives. Among various studied catalysts, two-dimensional (2D) materials show extraordinary electrocatalytic performance and are potential replacements for noble metals owing to their unique properties as HER catalysts. This review provides a concise appraisal of various 2D materials such as graphene, layered double hydroxides, metal carbides, chalcogenides and nitrides (MXenes), black phosphorus, and their unique electrochemical properties. In addition, the review presents the effect of various structural engineering protocols such as morphology, doping, defect engineering, and heterostructures in realizing high-efficiency hydrogen evolution. This timely review aims to bring forth the current development in the field of 2D material-based electrocatalysis and the future research pathway in the area of electrocatalysis.