Over a decade, the issue of globalization has continuously been a great concern because of the related adverse effects of climate change. This has prompted the engagement of many institutions to venture into sustainability as a tool to help respond to problems of climate change. Green finance has been identified as an important financial instrument for achieving the objective, through the issuance of green bonds to finance environmentally friendly projects. Since its first issuance in 2007, green bonds have continued to attract more investors and have seen exponential growth. Making it an important tool that can help the EU to achieve its 2030 climate and energy objectives, the UN Sustainable Development Goals, and the 2016 Paris Agreement on climate change, by enhancing the diversion of investment into green and sustainable projects with environmental benefits. However, to further enhance this rapid growth and strive towards achieving these long-term goals, have shed light on the legal and policy aspects associated with green bonds. Therefore, in this paper, we present the developments and functioning of the EU green bond market, its legal and policy issues, and various actors and players shaping the market. Thereby identifying critical issues restricting the development of the market and coming up with recommendations to help overcome these challenges, to further protect the integrity of the asset class, and encourage transparency within and outside the green bond market.