Sustainable finance is booming globally. Investors, governments and institutions are now demanding environmentally responsible, socially responsible, and good governance financial systems. These goals are generally quantified using environmental, social and governance (ESG) indicators. However, traditional finance systems can have issues like poor quality of data, lack of transparency and slow reporting and lack of trust in ESG scores. These issues are causing it to be difficult to measure sustainability in a reliable way. Financial technology (FinTech) is revolutionizing sustainable finance. New digital tools like artificial intelligence (AI), machine learning, big data and blockchain are now being used to collect, process and analyse ESG and climate related information. These tools are used to help investors and policymakers to make better and faster decisions. This review paper provides an overview of recent research on how FinTech can contribute to sustainable finance. It is focused on three main areas; ESG scoring and measurement AI-based climate risk assessment and digital platforms for green bonds and other sustainable debt instruments. The study is based on integrative approach of narrative review with a clear and transparent search process of the literature. Academic articles and important institutional reports that were published in the recent years are reviewed. The findings reveal that FinTech contributes to more efficiency, better data coverage and accessibility to sustainability information. At the same time, important challenges remain such as biased algorithms, unclear AI models, weak regulation and the risk of greenwashing. This review highlights these issues and suggests directions for future research to improve trust, transparency and ethical use of digital technologies in sustainable finance.