Environmental, Social, and Governance (ESG) criteria have emerged as pivotal metrics for evaluating corporate sustainability and guiding responsible investments. However, the complexity and heterogeneity of ESG data, coupled with evolving regulations, pose significant challenges for accurate assessment. The advent of deep learning (DL) offers transformative potential to address these challenges, leveraging advanced neural architectures to analyze vast and unstructured datasets, from financial reports to social media sentiment. This paper explores the intersection of DL and ESG, highlighting key opportunities such as enhanced prediction accuracy, automated unstructured data analysis, and optimized sustainable portfolios. It also critically examines the ethical and practical challenges, including environmental impacts, algorithmic biases, hallucinations and governance risks. By synthesizing existing literature and proposing pathways for responsible adoption, this study underscores the dual promise and pitfalls of DL in advancing ESG Criteria, advocating for a balanced approach that harmonizes technological innovation with sustainability principles.