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Non-Invasive Inspection (NII) has become a fundamental tool in modern industrial maintenance strategies. Remote and online inspection features keep operators fully aware of the health of industrial assets whilst saving money, lives, production and the environment. This paper conducted crucial research to identify suitable sensing techniques for machine health diagnosis in an NII manner, mainly to detect machine shaft misalignment and gearbox tooth damage for different types of machines, even those installed in a hostile environment, using literature on several sensing tools and techniques. The researched tools are critically reviewed based on the published literature. However, in the absence of a formal definition of NII in the existing literature, we have categorised NII tools and methods into two distinct categories. Later, we describe the use of these tools as contact-based, such as vibration, alternative current (AC), voltage and flux analysis, and non-contact-based, such as laser, imaging, acoustic, thermographic and radar, under each category in detail. The unaddressed issues and challenges are discussed at the end of the paper. The conclusions suggest that one cannot single out an NII technique or method to perform health diagnostics for every machine efficiently. There are limitations with all of the reviewed tools and methods, but good results possible if the machine operational requirements and maintenance needs are considered. It has been noted that the sensors based on radar principles are particularly effective when monitoring assets, but further comprehensive research is required to explore the full potential of these sensors in the context of the NII of machine health. Hence it was identified that the radar sensing technique has excellent features, although it has not been comprehensively employed in machine health diagnosis.