Drones as advanced cyber-physical systems are undergoing a transformative shift with the advent of vision-based learning, a field that is rapidly gaining prominence due to its profound impact on drone autonomy and functionality. Different from existing task-specific surveys, this review offers a comprehensive overview of vision-based learning in drones, emphasizing its pivotal role in enhancing their operational capabilities under various scenarios. We start by elucidating the fundamental principles of vision-based learning, highlighting how it significantly improves drones' visual perception and decision-making processes. We then categorize vision-based control methods into indirect, semi-direct, and end-to-end approaches from the perception-control perspective. We further explore various applications of vision-based drones with learning capabilities, ranging from single-agent systems to more complex multi-agent and heterogeneous system scenarios, and underscore the challenges and innovations characterizing each area. Finally, we explore open questions and potential solutions, paving the way for ongoing research and development in this dynamic and rapidly evolving field. With growing large language models (LLMs) and embodied intelligence, vision-based learning for drones provides a promising but challenging road towards artificial general intelligence (AGI) in 3D physical world.