It is known that since the Second World War, nanotechnology has represented an intellectual revolution from a scientific point of view and is now at the centre of the transformation mechanism of science and society. The study of nanoscience and nanotechnology has had a great impetus, generally speaking, since the 1950s. Research into nanomaterials and their applications has made great strides to date: new tools for manipulating matter have been developed and new materials have been obtained. Electron microscopes have been designed and progressively improved in their basic operating principle. Tunneling Electron Microscopy (TEM) has made it possible to analyse fine details in the structure of nanomaterials, while the Scanning Electron Microscope (SEM) has made it possible to acquire detailed images of the sample thanks to its greater resolving power. At the beginning of the 1970s, the Topografiner opened the way to Scanning Probe Microscopy (SPM). The development of this technique—with the Scanning Tunneling Microscope (STM) and Atomic Force Microscope (AFM)—allowed researchers to scan the surface of samples down to atomic size and manipulate individual atoms. In this field, scientists such as Gerd Binnig and Heinrich Rohrer (1933–2013), for example, who were awarded the Nobel Prize in 1986, came to the forefront of nanotechnology history. Laboratory techniques such as soft lithography, which uses elastomers to replicate structures, and physical and chemical vapour deposition, have been developed to obtain extremely high-quality materials. This chapter presents historical–scientific technical details on the historical–scientific development of scanning devices and laboratory techniques applied to nanotechnology. We also address the mathematics that underpins, from a theoretical point of view, some of the techniques presented.