A review is given on studies of statistics at small scales in turbulent flows from a view point of universality. It is assumed in the view that the statistics at sufficiently small scales in the absence of mean flow are at a certain kind of local equilibrium state, and the influence of the mean flow may be regarded as a perturbation added to the equilibrium state. This idea has been examined by comparison of spectral characteristics derived by the idea with those in turbulent boundary layers, mixing layers and direct numerical simulations (DNS) of homogeneous turbulent shear flow. The applicability of this idea to turbulent channel flows is discussed in the light of the data of the log-law region in DNS of turbulent channel flows with the friction Reynolds number Ret up to 5120.