This work presents a review on solution methods and analysis of nanoplates structures with different boundary conditions and load cases, under some effects such as magnetic field and the effect of the different parametric study on the vibration and analysis. Moreover, it represents a review about the theories that are used to study these nanoplates structures such; the nonlocal elasticity theory by Eringen which is introduced to take into consideration the small scale effect of such nano-structure. The equation of motion of the nanoplate is derived then it used to study this type of nano-structures. Nanoplates are used in a lot of branches of life and in different applications because of the high and excellent mechanical, thermal and electrical properties of these nanoplates. Applications of nanoplate structure are also introduced to show the importance of studying and getting a solution of such nanoplates. Also, some parametric studies are discussed to show the effect of the studied parameters on the dynamic behaviour and analysis of these nanoplates.