Different models of the magnetosphere are discussed critically. It is pointed out that there is a principal difference between the case when the impinging interplanetary plasma has no initial magnetization, B 0 = 0, (as in the Chapman-Ferraro theory), and the case when the plasma is initially magnetized, B 0 ≠ 0, even if B 0 is very small. In the former case the plasma remains unmagnetized (like a superconductor) and cannot penetrate into the magnetosphere. Therefore the plasma is separated by a sharp boundary from the magnetosphere, (“closed magnetosphere” model). In the latter case when the plasma is magnetized (which is more realistic) there is a possibility that field lines run from the earth to infinity (“open magnetosphere” model). Particles from the interplanetary space may penetrate into the magnetosphere. At the same time there may be a number of discontinuity surfaces of different character, such as the Cahill discontinuity. It is important to make terrella experiments in order to study the complicated phenomena occurring when a magnetized plasma penetrates into a dipole field.