Music transcription is the process of transforming recorded sound of musical performances into symbolic representations such as sheet music or MIDI files. Extensive research and development have been carried out in the field of music transcription and technology. This comprehensive review paper surveys the diverse methodologies, techniques, and advancements that have shaped the landscape of music transcription. The paper outlines the significance of music transcription in preserving, analyzing, and disseminating musical compositions across various genres and cultures. It also provides a historical perspective by tracing the evolution of music transcription from traditional manual methods to modern automated approaches. It also highlights the challenges in transcription posed by complex singing techniques, variations in instrumentation, ambiguity in pitch, tempo changes, rhythm, and dynamics. The review also categorizes four different types of transcription techniques, frame-level, note-level, stream-level, and notation-level, discussing their strengths and limitations. It also encompasses the various research domains of music transcription from general melody extraction to vocal melody, note-level monophonic to polyphonic vocal transcription, single-instrument to multi-instrument transcription, and multi-pitch estimation. The survey further covers a broad spectrum of music transcription applications in music production and creation. It also reviews state-of-the-art open-source as well as commercial music transcription tools for pitch estimation, onset and offset detection, general melody detection, and vocal melody detection. In addition, it also encompasses the currently available python libraries that can be used for music transcription. Furthermore, the review highlights the various open-source benchmark datasets for different areas of music transcription. It also provides a wide range of references supporting the historical context, theoretical frameworks, and foundational concepts to help readers understand the background of music transcription and the context of our paper.