Hydrogen is a prospective energy carrier because there are practically no gaseous emissions of greenhouse gases in the atmosphere during its use as a fuel. The great benefit of hydrogen being a practically inexhaustible carbon-free fuel makes it an attractive alternative to fossil fuels. I.e., there is a circular process of energy recovery and use. Another big advantage of hydrogen as a fuel is its high energy content per unit mass compared to fossil fuels. Nowadays, hydrogen is broadly used as fuel in transport, including fuel cell applications, as a raw material in industry, and as an energy carrier for energy storage. The mass exploitation of hydrogen in energy production and industry poses some important challenges. First, there is a high price for its production compared to the price of most fossil fuels. Next, the adopted traditional methods for hydrogen production, like water splitting by electrolysis and methane reforming, lead to the additional charging of the atmosphere with carbon dioxide, which is a greenhouse gas. This fact prompts the use of renewable energy sources for electrolytic hydrogen production, like solar and wind energy, hydropower, etc. An important step in reducing the price of hydrogen as a fuel is the optimal design of supply chains for its production, distribution, and use. Another group of challenges hindering broad hydrogen utilization are storage and safety. We discuss some of the obstacles to broad hydrogen application and argue that they should be overcome by new production and storage technologies. The present review summarizes the new achievements in hydrogen application, production, and storage. The approach of optimization of supply chains for hydrogen production and distribution is considered, too.