Machine Learning and AI in Modern Astronomy: A Review of Methods, Applications, Challenges, and a Reproducible Case Study

The exponential growth of astronomical data over the past two decades, driven by surveys such as the Sloan Digital Sky Survey (SDSS), the Gaia mission, and the upcoming Vera C. Rubin Observatory, has rendered traditional analytical methods insufficient for modern astrophysical research. Machine Learning (ML) and Artificial Intelligence (AI) have emerged as essential tools for processing this deluge, enabling automated systems that learn patterns, classify celestial objects, and predict cosmic phenomena. This paper provides a comprehensive review of ML and AI applications in astronomy. We discuss core methodological families supervised, unsupervised, and reinforcement learning, alongside deep learning architectures including convolutional neural networks (CNNs), recurrent neural networks (RNNs), and generative models. We then examine major application domains: galaxy morphology classification, exoplanet detection, transient and gravitational-wave identification, spectral analysis, cosmological structure mapping, and solar physics. To complement the literature review with a concrete demonstration, we include a fully reproducible case study on galaxy morphology classification. Using a synthetic dataset of 900 galaxy images across three morphological classes, we train and compare two lightweight machine learning baselines: a Random Forest classifier on Histogram of Oriented Gradients (HOG) features and a Multilayer Perceptron (MLP) on raw pixels, achieving 98.9% and 96.7% test accuracy, respectively. The companion Jupyter notebook also provides a PyTorch implementation of a small convolutional network for readers with GPU access. Finally, we discuss the central challenges of AI in astronomy data bias, model interpretability, overfitting, computational cost, and reproducibility and outline future directions, including explainable AI, real-time observatory pipelines, multi-messenger data fusion, and the democratization of AI tools through open infrastructure.