•The realization of commercial large-scale application of agricultural mobile platform is inseparable from its autonomous mobile capability.•The autonomous mobility is affected by the mobile structure and the navigation system.•The application of in facility agriculture is relatively mature, and the application in field is a challenging.•It is more mature for commercial application in agricultural harvesting tasks.•Nonstructural effects caused by plant shading and changes in topography and water flow have greater significance. With the gradual disappearance of the demographic dividend and the labor shortage brought by the aging population, it is necessary and urgent to achieve a high degree of automation in agricultural scenarios. And with the development of science and technology, it has made certain progress. The autonomous mobility of platform plays a very important role in this progress. It expands the point-to-point agricultural activities of a single plant into the entire agriculture scene. The autonomous mobility of platforms is driven by the considerable multiple scenarios with different requirements and the need for an adaptable and reliable system. It contains mobile structure and motion control, which complement each other. This paper gives a detailed introduction and summarizes the state-of-the-art agricultural mobile platforms, sensor-based autonomous positioning and navigation methods, as well as their practical applications in different specific agricultural scenarios, especially harvesting task. It accounts for the absolute amount of labor in the overall agricultural task. Unlike, traditional industrial and urban, the agricultural scenarios have more unstructured complex environment. High autonomous mobility of the agricultural mobile platform, which requires the installation of more complex and comprehensive sensors sensitively perceive scene information and more intelligent positioning and navigation strategy, enable the mobile platform to securely, flexible perform agricultural tasks. Therefore, special attention is paid to the navigation strategy and mobile cruise strategy based on various sensor, to improve the autonomy of agricultural mobile platforms. It's potential challenges and future are prospected based on the development trend of agricultural mobile platforms.