Applications of non-invasive sensing techniques to investigate the internal structure and surface of precious and delicate objects represent a very important and consolidated research field in the scientific domain of cultural heritage knowledge and conservation. The present article is the first of three reviews focused on contact and non-contact imaging techniques applied to surveying cultural heritage at micro- (i.e., manufacts), meso- (sites) and macro-scales (landscapes). The capability to infer variations in geometrical and physical properties across the inspected surfaces or volumes is the unifying factor of these techniques, allowing scientists to discover new historical sites or to image their spatial extent and material features at different scales, from landscape to artifact. This first part concentrates on the micro-scale, i.e., inspection, study and characterization of small objects (ancient papers, paintings, statues, archaeological findings, architectural elements, etc.) from surface to internal properties.