Efficient and sustainable crop production process management is crucial to meet the growing global demand for food, fuel, and feed while minimizing environmental impacts. Traditional crop management practices, often developed through empirical experience, face significant challenges in adapting to the dynamic nature of modern agriculture, which is influenced by factors such as climate change, soil variability, and market conditions. Recently, reinforcement learning (RL) and large language models (LLMs) bring transformative potential, with RL providing adaptive methodologies to learn optimal strategies and LLMs offering vast, superhuman knowledge across agricultural domains, enabling informed, context-specific decision-making. This paper systematically examines how the integration of RL and LLMs into crop management decision support systems (DSSs) can drive advancements in agricultural practice. We explore recent advancements in RL and LLM algorithms, their application within crop management, and the use of crop management simulators to develop these technologies. The convergence of RL and LLMs with crop management DSSs presents new opportunities to optimize agricultural practices through data-driven, adaptive solutions that can address the uncertainties and complexities of crop production. However, this integration also brings challenges, particularly in real-world deployment. We discuss these challenges and propose potential solutions, including the use of offline RL and enhanced LLM integration, to maximize the effectiveness and sustainability of crop management. Our findings emphasize the need for continued research and innovation to unlock the full potential of these advanced tools in transforming agricultural systems into optimal and controllable ones.