Scientific research of art objects is not limited to the analysis of samples. The object has to be studied and a problem should be defined accurately before samples are taken for analysis. The methodology for the investigation of paintings is described from microscopic examination to the analysis of samples using various methods. Potentialities and limitations of the examination of paint cross sections are discussed. Disadvantages are the slight damage to the painting and the stratigraphic risk that the layer structure in the sample is not representative of its surroundings. Pigments, media, and painting technique can be derived to a great extent from microscopic examination, but the color of a layer, let along the original color is hard to pinpoint, because of patination of the surface and because of the different in illumination. Analytical methods to be applied to the surface of a cross section are laser microspectral analysis and microchemical coloring reactions for synthetic organic pigments. The analysis of binding media in stratified paint samples is difficult if it has to be unambiguous. Materials from adjacent layers can interfere or may even have penetrated. Staining and heating tests on microtome slices or cross sections have positive results under favorable conditions. A global differentiation of the main groups of media is feasible. Limitations of analytical possibilities are brought about by, for example, small sample size, complexity of a mixture, chemical change in the sought component due to aging, interference of impurities, and a lack of proper reference material. Dating <i>post quem</i> or in a few cases <i>ante quem</i> is often possible, sometimes ruling out a certain artist. Authenticity cannot be proven by chemical analysis.