Relying on theory and empirical analysis, we study the real effects and pricing of Sustainability Linked-Bonds (SLBs). Post-issuance, SLB issuers decarbonize about 6 percentage points faster than non-issuers. Our theoretical framework helps understanding SLBs' incentive structure and their pricing. Using a novel mispricing measure, we test several empirical predictions of the model. Overpriced SLBs at issuance experience negative secondary market returns. Stock markets react more positively to overpriced SLB issues that are large, suggesting a wealth transfer from bondholders to shareholders. Finally, SLBs' mispricing increases with firms' ESG ratings. Overall, our analysis shows that SLBs have meaningful implications for firms' decarbonization and financial markets.