The review of studies on memristive properties or effect of resistive switchings in four classes of high temperature superconductors (HTSCs): Bi2Sr2CaCu2O8+y (BSCCO), is presented in order to reveal functional properties of HTSCs which become apparent in the effects under discussion, prospects of usage of HTSC based memristors in applications and search for new mechanisms of strongly correlated nature to realize new generation memristors. The properties are: undergoing metal insulator transition at oxygen doping, transport anisotropy, existence of charge reservoirs through which doping of conductive copper oxygen plays is carried out. These are the main functional properties of HTSCs which permit to use them in memristors. By the example of study of bipolar effect of resistive switching in HTSC based heterojunctions it is shown how one can form memristor structures based on HTSCs using their functional properties.