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One of the basic concepts of modern physics with a long prehistory is a fluid, which means a substance that flows under an applied shear stress. In this sense fluids form a wide subset of the phases of matter that includes liquids, dense gases, plasmas, and to some extent even plastic solids. Fluidity is one of the main dynamical characteristics that depends strongly on the details of the local structure. And vice versa, dominant details of local structural ordering in the arrangement of particles on some time scales are important for understanding the dynamics of fluids. The orderliness over distances comparable to the inter-particle distances is usually treated as the short-range order, whereas the orderliness repeated over infinitely large distances is called the long-range order. Both are absent in the ideal gas, but liquids and amorphous solids exhibit the short-range order. The physics of crystalline solids with the long-range order is well understood. In fluids, however, the atomic structure is changing with time. How are specific features of structural ordering reflected in the fluid dynamics? In this chapter we try to find answers to some old and new questions that still make the fluid dynamics still very attractive for the theoretical studies.