•Discusses the stages of development of questioned document analysis techniques.•The transformation of chromatographic methods is shown.•The prospects for the development of spectral methods are described.•Examples of successful work to multidimensional data processing area are given. Dating an inscription on a sheet of paper by analyzing the dye is one of the most important and complex forensic tasks. To date, the task of analyzing the limitation of document details has not been fully resolved. Currently, the main research trend in the field of dating is the use of various chromatography methods. They are based on the study of the evaporation dynamics of volatile ink components. Basically, such methods are used within 2 years of the stroke of the writing composition. In addition to traditional gas chromatography, researchers use all known separation methods to determine the age, including ion chromatography, high-performance liquid chromatography, thin-layer chromatography, and gas chromatography-mass spectrometry. The review analyzes the most authoritative European studies in this area and discusses the reasons behind the limitations of chromatographic methods. An alternative to chromatographic studies of volatile components are spectral methods for the analysis of dyes. The most interesting works carried out by the methods of mass spectrometry, microspectrophotometry, Raman spectroscopy, diffusion of luminescence in the near-infrared and visible regions, laser-induced breakdown spectroscopy, Fourier-transform infrared spectroscopy, etc. are described. Despite a number of successful works in this area, the desired result has also not yet been achieved in terms of the accuracy and reliability of the results. The advantages and disadvantages of the methods are analyzed. Modern researchers are beginning to actively use new methods of mathematical processing of digital signal arrays. Examples of the use of chemometric data processing, including principal component analysis, are presented.