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The present manuscript makes an extensive review of the scientific approaches developed in the last decade involving infrared and Raman spectroscopy combined with chemometrics for solving several issues in the investigation of the most relevant forensic traces, such as questioned documents and currency, explosives, gunshot residues, illicit drugs and body fluids. In addition, current trends, main challenges and the adequate use of several chemometric techniques are discussed. Principal component analysis (PCA) was found to be the most used technique. This unsupervised approach, however, has sometimes been misunderstood as a classification technique. Discriminant analysis techniques are widely employed, leaving a range of possibilities for application of class-modeling techniques, particularly in cases of problems regarding only one target class. In addition, increasingly complex dataset structures frequently require nonlinear approaches or flexible techniques such as multivariate curve resolution-alternating least squares (MCR-ALS). Results reporting, however, still lack reliable quality parameters and sample representativeness, posing a significant challenge to the solution of forensic problems. Regarding the analytical techniques, Raman has been playing an important role, especially in the area of questioned documents and of body fluids. Portable and hyperspectral imaging infrared spectrometers have also been showing significant potential in forensic applications.

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