Despite the fact that green insurance makes up a significant portion of green finance, there is a lack of systematic understanding and analysis on the international green insurance market in the literature. In this paper, we study how the market for green insurance has evolved and discuss the current challenges. The important elements promoting sustainable growth in the market include universal consensus on the definition of green insurance, an optimal regulatory framework, technological advancement, and talent nurturing, and rising social acceptance. We apply the institutional framework to explore the future direction of market reform for a sustainable market. Reinforcing the three institutional pillars will help to address the current deficiencies in the market. The pollution liability market in China is examined as a case study. This paper gives insight to both academic and industry fields on drivers and challenges in the increasingly complex and fast-growing green insurance market.