Magnetization sensitive second harmonic generation (MSHG) is a nonlinear optical technique that, due to the dipole selection rules, is specifically sensitive to surfaces and interfaces of centrosymmetric media. This surface/interface sensitivity of MSHG in combination with very large magneto-optical effects lead to a fast development of this technique over the past decade. The main attention of the present review is on the application of the MSHG technique to magnetic thin films and surfaces, with a focus on the achieved progress in understanding, with the help of MSHG, of the magnetic surface and interface phenomena. On the one hand, an extreme sensitivity of MSHG to the electronic and magnetic structure of clean surfaces has been successfully demonstrated. On the other hand, the penetration depth of light allowed one to use this sensitivity to study buried interfaces in multilayer systems. Various phenomena, such as surface states on magnetic metals, enhanced magnetic moments of low-coordinated atoms, and quantum well states, have been studied. Further experimental developments of the MSHG technique, like space- and time resolution as well as magnetization sensitive sum frequency generation, appear to be promising as well.