The pure shear tensors play a significant role in continuum mechanics. Recent authors' results concerning some remarkable properties of pure shear tensors and their sets are presented. A list of the properties defining pure shears is quoted. The properties of the whole set of all pure shears are described. An extraordinary role of the pure shears in the linear theory of elasticity is disclosed. A new approach, in terms of Kelvin moduli and pure shears as proper elastic states, to the description of the symmetries of elastic materials is proposed. Finally, it is shown that a two-parametric set of orthonormal bases of deviatoric space consisting solely of pure shears can be constructed.
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