The preservation and digitization of ancient Vedic texts inscribed on palm leaves hold immense cultural and historical significance. However, recognizing handwritten text in these manuscripts is a complex task due to diverse handwriting styles, script intricacies, and material degradation. This systematic literature review examines the application of machine learning techniques to the recognition of handwritten Vedic texts on palm leaves. The review analyzes state-of-the-art approaches, including traditional machine learning algorithms and advanced deep learning models. It explores preprocessing techniques, feature extraction methods, and the role of annotated datasets in addressing challenges posed by the unique characteristics of palm leaf manuscripts. The findings indicate significant progress in leveraging machine learning for ancient text recognition, but challenges such as limited dataset availability, script variability, and degraded manuscript quality persist. This review identifies gaps in current research and proposes directions for future work, including the development of comprehensive datasets, culturally tailored algorithms, and interdisciplinary collaborations. By synthesizing the existing body of knowledge, this paper provides valuable knowledge for researchers and practitioners seeking to advance the field of ancient manuscript recognition and contribute to the preservation of invaluable heritage.