Integrating Artificial Intelligence (AI) techniques with remote sensing holds great potential for revolutionizing data analysis and applications in many domains of Earth sciences. This review paper synthesizes the existing literature on AI applications in remote sensing, consolidating and analyzing AI methodologies, outcomes, and limitations. The primary objectives are to identify research gaps, assess the effectiveness of AI approaches in practice, and highlight emerging trends and challenges. We explore diverse applications of AI in remote sensing, including image classification, land cover mapping, object detection, change detection, hyperspectral and radar data analysis, and data fusion. We present an overview of the remote sensing technologies, methods employed, and relevant use cases. We further explore challenges associated with practical AI in remote sensing, such as data quality and availability, model uncertainty and interpretability, and integration with domain expertise as well as potential solutions, advancements, and future directions. We provide a comprehensive overview for researchers, practitioners, and decision makers, informing future research and applications at the exciting intersection of AI and remote sensing.