Direction of arrival (DOA) estimation is a significant technology in navigation and positioning systems. With the development of machine learning, DOA estimation methods based on machine learning have shown great potential in indoor and outdoor navigation. This paper reviews the theoretical background and models of DOA and gives an overview of machine learning methods applied to DOA estimation. It also discusses DOA estimation methods based on machine learning and their applications in navigation. Machine learning can be divided into traditional machine learning methods, deep learning methods, and reinforcement learning methods. Traditional machine learning methods are support vector machines, k-nearest neighbor classification, etc. Deep learning methods consist of deep neural networks, convolutional neural networks, etc. By analyzing the challenges faced by current applications and future development directions, potential strategies for enhancing the performance of DOA estimation are proposed. This study aims to provide a comprehensive technical framework and a reference for future research for researchers in related fields.