Environmental, social, and governance (ESG) funds are among the fastest-growing investment styles. ESG investing thereby has a governing effect, and a key open question is whether ESG merely reduces risks for investors or whether it can have a sustainability impact and actively contribute to climate transition. This governance through ESG is characterized by three potential transmission mechanisms: ratings, shareholder engagement, and capital allocation. These can create sustainability impact or constitute “ESG gaps” if transmission mechanisms remain ineffective/unutilized. Based on financial data, an investigation of ESG methodologies and expert interviews, we provide a novel ESG market analysis, focusing on the standard-setting role of a handful of ESG index providers in capital allocation. Our findings highlight that while “Dark Green” indices could have an impact, currently “Broad ESG” indices, which do not meaningfully facilitate sustainability, dominate investing: we call this the “ESG capital allocation gap.” This has important implications, because effective transmission mechanisms are crucial for ESG funds to achieve sustainability impact in the real economy.