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The symmetry-based study of MS₂ (M=Mo, W) single-wall nanotubes (SWNTs) is reviewed. First, the structure and symmetry of MS₂ NTs is determined. Then, conserved quantum numbers and general forms of potentials are derived. The valence force-field method implemented into the POLSym code is used to calculate phonon dispersions. Phonons characterized by a zero angular-momentum quantum number are studied in detail. The functional dependence of the frequency of rigid layer modes on NT diameter and chirality are found, and Raman- and infrared-active modes are singled out. Electronic band structure calculations are performed by the symmetry-based density functional tight-binding (DFTB) method. Changes in the band-gap type and size with NT chirality and diameter are evaluated. Optical absorption spectra of individual NTs are calculated using DFTB wave functions for exact transition matrix element calculations. Diffraction patterns of MS₂ are predicted and NT characterization by different diffraction methods is discussed. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim