This paper takes a comprehensive look at Artificial Intelligence (AI)-based weather forecasting models and focuses on the current status, challenges, and directions for further development. A review of nearly 40 models proposed primarily after 2015 highlights the importance of critically examining various aspects of AI-based weather forecasting models, including Machine Learning (ML) techniques, datasets, predictand parameters, extreme weather forecasting capability, lead time, spatiotemporal scale, performance criteria, and in-depth analysis of state-of-the-art models from different perspectives. Unlike previous reviews that have targeted only a limited number of models or features, this study focuses on different aspects of current AI-based models. Some important characteristics of AI-based models are computational efficiency and forecasting speed. However, challenges such as limited historical data and quality, model explainability, extreme weather forecasting, physical constraints, temporal adaptation, generalization, and uncertainty remain. Addressing these challenges is essential to enhance the effectiveness and reliability of AI-based weather forecasting across different weather conditions.