Due to the involvement of high portion of atomic coordination imperfection in surfaces and interfaces, the properties of magnetic nanocrystals dramatically differ from that of the corresponding bulk counterparts, which have led to a surge in both experimental and theoretical investigations in the past decades. This review summarizes the studies for these size-dependent magnetic properties, and additional thermal or phase stabilities, and mechanical properties. To interpret the above phenomena, a thermodynamic model for the size dependence and interface dependences of these properties is described, which is based on Lindemann s criterion for melting, Mott s expression for the vibrational melting entropy, and Shi s model for the size-dependent melting temperature. The model without any adjustable parameter is confirmed by a large number of experimental results, and helps us to understand the structures and properties of the magnetic nanocrystals. Moreover, other theoretical works on the above properties are also mentioned and commented.