The paper contains a short literature review on the subject of special type of thin film structures with resistive-switching memory effect. In the literature, such structures are commonly labeled as "memristors". The word "memristor" originates from two words: "memory" and "resistor". For the first time, the memristor was theoretically described in 1971 by Leon Chua as the 4th fundamental passive electronics element with a non-linear current-voltage behavior. The reported area of potential usage of memristor is enormous. It is predicted that the memristor could find application, for example in the domain of nonvolatile random access memory, flash memory, neuromorphic systems and so forth. However, in spite of the fact that plenty of papers have been published in the subject literature to date, the memristor still behaves as a "mysterious" electronic element. It seems that, one of the important reasons that such structures are not yet in practical use, is unsufficient knowledge of physical phenomena determining occurrence of the switching effect. The present paper contains a literature review of available descriptions of theoretical basis of the memristor structures, used materials, structure configurations and discussion about future prospects and limitations.