This review systematically examines deep learning applications in financial asset management. It identifies how these applications contribute to various financial activities and areas ripe for future research. We use the Scopus database to select the most relevant articles published from 2018 to 2023. The inclusion criteria encompassed articles that explicitly apply deep learning models within financial asset management. We excluded studies focused on physical assets. This review also outlines our methodology for evaluating the relevance and impact of the included studies, including data sources and analytical methods. Our search identified 934 articles, with 612 meeting the inclusion criteria based on their focus and methodology. The synthesis of results from these articles provides insights into the effectiveness of deep learning models in improving portfolio performance and price forecasting accuracy. The review highlights the broad applicability and potential enhancements deep learning offers to financial asset management. Despite some limitations due to the scope of model application and variation in methodological rigour, the overall evidence supports deep learning as a valuable tool in this field. Our systematic review underscores the progressive integration of deep learning in financial asset management, suggesting a trajectory towards more sophisticated and impactful applications. Future research should explore the capabilities of these models for diverse financial contexts.