Ionospheric irregularities and variability can significantly impact various applications, such as satellite communications, navigation, and remote sensing. Accurately characterizing and forecasting ionospheric conditions are therefore essential for mitigating their effects. Advances in machine learning techniques have led to the development of powerful models for ionospheric modeling and forecasting. This comprehensive review synthesizes the cutting-edge Machine Learning (ML)-based approaches for ionospheric studies, covering a broad spectrum of approaches that includes supervised learning, unsupervised learning, and deep learning. The review discusses the advantages and limitations of different approaches, provides insights into model performance, and highlights key challenges and future research directions. A particular focus is given to the development of global ionospheric models using machine learning, which has the potential to revolutionize ionospheric monitoring and forecasting.