Abstract: In recent years, deep learning has achieved remarkable progress in meteorological forecasting and climate modeling, exerting a growing influence on agricultural applications. While numerous review articles have systematically examined related methodologies, most focus on model architectures, task types, or application domains, with limited attention given to the agricultural perspective. This paper provides a comprehensive review of the development of Large Meteorological Models (LMMs), structured around model architecture. We trace the evolution from traditional numerical methods to deep learning approaches and categorize existing models into six major classes: classical deep neural networks, graph neural networks, Transformer-based architectures, state space models, generative models, and physics-informed/multimodal fusion models. Furthermore, we summarize representative applications of LMMs in agriculture, including meteorological forecasting services, extreme weather early warning and disaster mitigation, and decision support systems for precision agriculture. We also examine commonly used datasets and evaluation metrics in the field. This is followed by a discussion of current challenges, particularly in areas of generalization capability, uncertainty quantification, and physical consistency. Finally, we outline key research directions for future exploration in this rapidly evolving field. This work aims to provide a systematic reference for advancing both the research and application of LMMs in agricultural contexts.