Financial AI empowers sophisticated approaches to financial market forecasting, portfolio optimization, and automated trading. This survey provides a systematic analysis of these developments across three primary dimensions: predictive models that capture complex market dynamics, decision-making frameworks that optimize trading and investment strategies, and knowledge augmentation systems that leverage unstructured financial information. We examine significant innovations including foundation models for financial time series, graph-based architectures for market relationship modeling, and hierarchical frameworks for portfolio optimization. Analysis reveals crucial trade-offs between model sophistication and practical constraints, particularly in high-frequency trading applications. We identify critical gaps and open challenges between theoretical advances and industrial implementation, outlining open challenges and opportunities for improving both model performance and practical applicability.