As the number of malware attacks continues to grow year by year with increasing complexity, Android devices have remained vulnerable with over 30 million mobile attacks detected in 2023. Thus, it has become more challenging to detect recent malware using traditional methods, such as signature-based and heuristic-based methods. Meanwhile, there has been a rise in the application and research of machine learning (ML) and deep learning (DL). As a result, researchers have proposed ML- and DL-based methods for Android malware detection. This paper reviews the methods proposed in the literature for Android malware detection using DL. It establishes a taxonomy highlighting and explores the feature types extracted through static and dynamic analyses and the DL models used in the literature. It also illustrates which feature types have been used with the different DL models. Finally, it discusses major challenges and potential future directions in the field of ML and DL methods for Android malware detection such as the need for updated datasets, more on-device evaluation of the methods and more approaches using dynamic/hybrid analyses. © The Author(s) under exclusive licence to The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden 2024.