The subject is aimed at the explanation of physical principles of diagnostics of 1D and 2D nanostructures suitable for a study of morphological and structural parameters, as well as of their local properties. The individual methods, fundamentals of their selection and optimization with respect with their lateral resolution will be described. In addition to scanning probe microscopic metods (STM, AFM, EFM, MFM, SNOM, etc.) and electron and ion microscopy (TEM, SEM, etc.) also optical microscopic spectroscopic techniques (e.g. confocal scanning Raman spectroscopy and photoluminiscence) and their combination will be discussed (STL, cathodoluminiscence, TERS, etc.). These methods will be demonstrated and tested as well.