The present article is a review of phenomena connected with neutrino oscillations. Mixing of two neutrinos (Majorana as well as Dirac) with masses ml and m2 is considered in detail. It is shown that the hypothesis of lepton mixing is not in contradiction with the existing data if \m\ — m\\ ;$ 1 (eVJ. Possible experiments designed to reveal neutrino oscillations at reactor, meson factory and high energy accelerator facilities are considered. In such experiments oscillation might be found if \m\ — m\\ > 0.01 (eVJ. The possibilities of searching for oscillations by experiments on cosmic ray neutrinos and especially on solar neutrinos are discussed in detail. The last experiments have an incredible high sensitivity from the point of view of testing the lepton mixing hypothesis (oscillation effects might be observable if \m\ — m\\ > 102 (eVJ). The "solar neutrino puzzle" is also discussed from the point of view of lepton mixing. Neutrino oscillations are considered then in the case where in nature there exist N > 2 neutrino types. In conclusion the case of heavy lepton mixing is considered. It is shown that in a concrete scheme with right-handed currents, the probabilities of such processes as \i -> ey, \i -* 3e etc. can be close to existing experimental upper limits, provided the heavy lepton masses are of an order ofa fewGeV, whereas the probabilities of the above processes are entirely negligible if only neutrinos are mixed.