Hydrogen has emerged as a promising climate-neutral energy carrier able to facilitate the processes of the European Union (EU) energy transition. Green hydrogen production through the electrolysis process has gained increasing interest recently for application in various sectors of the economy. As a result of the increasing renewable energy developments in the EU, hydrogen is seen as one of the most promising solutions for energy storage challenges; therefore, the leading countries in the energy sector are heavily investing in research of the technical obstacles for hydrogen applications and assessment of the current hydrogen market, which in turn leads to the acceleration of the upscaling of hydrogen production. The main objective of this article was to provide a comprehensive overview of various green hydrogen production, transportation and industrial application technologies and challenges in Europe, with a separate analysis of the situation in Lithuania. Various water electrolysis technologies and their production costs are investigated, along with recent developments in storage and transportation solutions. In addition, the performances and limitations of electrochemical processes are presented and analysed, research trends in the field are discussed and possible solutions for performance and cost improvements are overviewed. This paper proposes a discussion of perspectives in terms of future applications and research directions.