This paper has been written following the two lectures given by the author on the same subject at the CLXXV Course Radiation and Particle Detectors, of the International “E. Fermi” School in Varenna, but should not be considered in itself a comprehensive text on the subject. The basic principles of Ion Beam Analysis (used to deduce the composition of a target material) and of Accelerator Mass Spectrometry (used to deduce the concentration of rare isotopes in a sample) are recalled, and the solutions implemented for their application in the field of Cultural Heritage are described. In particular, the specific requirements for the detectors and for some beam control systems along the lines of the accelerator are discussed in some detail.