New phenomena - the first order magnetic phase transitions were observed in nanoclusters and nanostructures. For isolated ferrihydrite nanoclusters (d similar to 1-2 nm) in porous materials, for alpha-,gamma-Fe2O3 nanoclusters (d similar to 20-50 nm) and for composites of nanostructured metallic Eu with additives of alpha-, gamma-Fe2O3 nanoclusters and adamantane the critical temperatures (T (C), T (N)) and magnetic cluster critical sizes (R (cr)) were determined by means of thermodynamic models and Mossbauer spectroscopy. The first order magnetic phase transitions (jump-like) proceed by such a way when magnetization and magnetic order disappear by jump without superparamagnetic relaxation. According to thermodynamic model predictions the cluster and interface defects were suggested to play the main role in magnetic behavior. Thus, for the defective alpha-, gamma-Fe2O3 nanoclusters, at R <= R (cr), the presence of the first order (jump-like) magnetic phase transition was described in terms of magnetic critical size of cluster. The action of high pressure (up to 2 GPa) with shear (120-240 degrees) was effective for defect generation and nanostructure formation. For nanosystems including iron oxide nanoclusters, adamantane and metallic europium and subjected to shear stress under high pressure loading the critical value of defect density was estimated by the study of the character of magnetic phase transition. First-to-second-order (nanostructured metallic Eu) and second-to-first-order (alpha-, gamma-ferric oxide nanoclusters) changes of the character of magnetic phase transition were shown to accompany by the variation of critical temperatures compared to the corresponding bulk values.