Hydrogen, widely recognized as an efficient and clean energy carrier, holds significant promise for transforming future energy systems. Despite advances in hydrogen production and cost reduction, challenges in hydrogen storage continue to impede its widespread adoption. Traditional storage methods, such as high-pressure tanks and liquid hydrogen, have limitations related to high energy and resource costs. Solid-state materials offer a safer and more reliable alternative for hydrogen storage under various operating conditions. This review article provides an in-depth analysis of hydrogen storage materials, focusing on metal hydrides, complex hydrides, and carbon-based materials, with particular attention to their thermodynamic, structural, and kinetic properties. Additionally, the article explores the potential application of certain materials in Kazakhstan's hydrogen market, highlighting the country's rich mineral resources and existing industrial infrastructure. By leveraging these resources, Kazakhstan can play a crucial role in advancing hydrogen storage technologies and contributing to global decarbonization efforts. The review aims to offer comprehensive insights into the current state and prospects of solid-state hydrogen storage materials, emphasizing their relevance and potential impact on Kazakhstan's energy sector.