This chapter discusses how the sustainable debt market has grown from the first climate awareness bond in 2007 to a distinct asset class with a global volume of over USD 4 trillion in 2024. The largest share of instruments, referred to as GSS (green, social, and sustainability) bonds, are structured with a ‘use-of-proceeds’ clause for issuers to finance specific sustainable projects. As companies increasingly pledged climate targets, sustainability-linked bonds (SLBs) emerged. These instruments provide an incentive mechanism for issuers to achieve sustainability targets, thus holding issuers financially accountable for their sustainability commitments. But what factors influence companies' decisions to issue GSS bonds or SLBs? How are these instruments structured and priced? Do they effectively facilitate the financing of green projects and ensure that companies adhere to their sustainability targets? To understand the complexities of these questions and the evolution of the sustainable debt market, this chapter provides a comprehensive review of the relevant academic literature and offers a historical analysis of market development organized into four distinct phases. The chapter includes case studies to illustrate underlying market dynamics. Additionally, it discusses criticism regarding the limitations of SLBs' incentive mechanism and transparency. Finally, it concludes with policy recommendations and suggestions for future research.