This paper presents a comprehensive review of the advancements in Optical Music Recognition (OMR) driven by Deep Learning (DL) techniques. OMR aims to digitize music scores, transforming them into structured formats to enhance accessibility, facilitate preservation, and enable automated analysis. While early methods were based on heuristic approaches, the adoption of DL has revolutionized the field, achieving remarkable improvements in tasks such as layout analysis, symbol recognition, and music transcription. This survey offers a detailed examination of recent DL-based approaches, providing an in-depth analysis of datasets, evaluation metrics, methodologies, and results. Additionally, it explores emerging trends, identifies key challenges, and proposes future directions to advance OMR research. Despite the substantial progress achieved, critical challenges remain, highlighting the need for continued innovation and positioning this review as a valuable reference for both new and experienced researchers in OMR.