The identification of medicinal plant species from leaf imagery has attracted sustained scientific attention, motivated by the global dependence on botanical remedies and the limitations of expert-reliant manual methods. This paper offers a systematic review of machine learning (ML) and deep learning (DL) strategies for medicinal leaf analysis, with particular depth on deep learning architectures. Classical ML techniques — Support Vector Machines (SVM), Random Forest (RF), K-Nearest Neighbor (KNN), Naive Bayes (NB), and Decision Trees (DT) are examined alongside hand-engineered feature extraction approaches including Gray-Level Co-occurrence Matrix (GLCM), Histogram of Oriented Gradients (HOG), Local Binary Patterns (LBP), and geometric shape descriptors. Deep learning models covered in depth include AlexNet, VGG-16, InceptionV3, ResNet-50, MobileNetV2, DenseNet-121, and EfficientNet. A unified performance comparison is presented using accuracy, precision, recall, and F1-score across all reviewed approaches. The analysis shows that DL models attain up to 98.20% classification accuracy and 98.05% F1-score, substantially exceeding the strongest traditional ML baseline Random Forest at 93.80% accuracy and 92.85% F1-score. Persistent challenges including data scarcity, inter-species morphological overlap, domain shift, and model transparency are discussed, along with emerging research directions in self-supervised learning, explainable AI, and edge-deployable architectures.