Interdiffusion between two nanomaterials (NMs), A and B, occurs mainly inside the wide network of GBs, which are simultaneously the sources and sinks of vacancies. Partial GB diffusion fluxes of both A and B components directed to one another govern the conditions for low-temperature interdiffusion. The inequality of A and B GB partial diffusion coefficients initiates the GB Kirkendall and Frenkel effects and low-temperature phase formation in the grain interiors without participation of bulk diffusion. These phenomena are accompanied by generation and relaxation of stresses and degradation of nano-scale structure. The kinetics and mechanisms of these processes are controlled by the interdiffusion along stationary and migrating GBs. The size-dependent kinetics of GB interdiffusion phenomena in NMs can be described using two dimensionless parameters: delta/l for stationary GBs (l is the size of structural element, delta is the GB width) and lambda/l for migrating GBs ( lambda = (sDb delta / Vb)1/2 is the characteristic diffusion length, Db is the GB diffusion coefficient, Vb is the GB velocity, s is the segregation factor). The criteria, which allow predicting the minimum temperature of low-temperature phase formation depending on GB diffusivity, the velocity of GB migration, and time dependence of the size of structural element have been formulated and confirmed experimentally for different nano-objects. The mechanisms and models of GB interdiffusion phenomena in NMs have been proposed for analysis of experimental data.