Continuous crop monitoring enables the early detection of field emergencies such as pests, diseases, and nutritional deficits, allowing for less invasive interventions and yielding economic, environmental, and health benefits. The work organization of modern agriculture, however, is not compatible with continuous human monitoring. ICT can facilitate this process using autonomous Unmanned Ground Vehicles (UGVs) to navigate crops, detect issues, georeference them, and report to human experts in real time. This review evaluates the current state of ICT technology to determine if it supports autonomous, continuous crop monitoring. The focus is on shifting from traditional cloud-based approaches, where data are sent to remote computers for deferred processing, to a hybrid design emphasizing edge computing for real-time analysis in the field. Key aspects considered include algorithms for in-field navigation, AIoT models for detecting agricultural emergencies, and advanced edge devices that are capable of managing sensors, collecting data, performing real-time deep learning inference, ensuring precise mapping and navigation, and sending alert reports with minimal human intervention. State-of-the-art research and development in this field suggest that general, not necessarily crop-specific, prototypes of fully autonomous UGVs for continuous monitoring are now at hand. Additionally, the demand for low-power consumption and affordable solutions can be practically addressed.