Medical image classification, a critical component in medical diagnostics, has significantly advanced through the integration of machine learning (ML) and deep learning (DL) techniques. This review comprehensively explores the evolution, methodologies, and applications of ML and DL in medical image classification. Traditional ML methods, including support vector machines and decision trees, have provided a foundation for early advancements by utilizing handcrafted features. However, the advent of DL, particularly convolutional neural networks (CNNs), has revolutionized the field by enabling automatic feature extraction and achieving superior performance. This review examines various DL architectures, such as ResNet, VGG, and Inception, highlighting their contributions to tasks like tumor detection, organ segmentation, and disease classification. Furthermore, it addresses challenges like data scarcity, interpretability, and computational demands, discussing potential solutions like data augmentation, transfer learning, and model optimization. The review also considers the ethical implications and the need for robust validation to ensure clinical applicability. Through a comparative analysis of existing studies, this review underscores the transformative impact of ML and DL on medical imaging, emphasizing the continuous need for innovation and interdisciplinary collaboration to enhance diagnostic accuracy and patient outcomes.