Size-dependent effects (SDE, i.e. the characteristic size influence  of grains, particles, phase  inclusions, layers/laminates, pores, etc., on the properties of materials and substances have been studied in physics, chemistry and materials science for a long time. The development of advanced nanotechnology manifests some new problems such as the SDE identification in nanometer interval.  The SDE role in nanostructured (nanocrystalline, nanophase or nanocomposite) materials is of great importance both  for fundamental considerations and modern technology. The effect of the nanoparticle/nanocrystalline size on surface energy, melting point, phase transformations and phase equilibriums is considered as applied to nanostructured materials. The role of size-dependent effects in phonon, electronic, superconducting, and mechanical properties is also analysed. Special attention is paid to the contribution of other factors such as the interface structure, grain boundary segregations, residual stresses and pores,  non-uniform distribution of grain zise, and so on. The most interesting examples of the interface effect on the melting point (superheating) and strength/ductility of nanomaterials are described in detail. In particular, the importance of computer experiments and the study in situ of nanosubjects in high-resolution transmission electron microscopy is pointed. The little explored and unressolved  problems are pointed and discussed.                                                                                                                                                                                               

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