In the article we discusse the shortcomings of the classical approach to design of time machine based on the idea of closed timelike curves. The necessity of using quantum mechanics is discussed. The A.D. Alexandrov’s axiomatics of quantum mechanics is given. Different constructions of the so-called quantum time machines such as Svetlichny’s effictive time machine using quantum teleportation, quantum AAPV-time machine, Gray’s time ìachine, non-Gedel time machine are given. One is demonstrated as in using quantum time machines, time paradoxes are resolved.