Recently, memristor (anion-based memristor) is referred to as the fourth circuit element which resistance state can be gradually changed by the electric pulse signals that have been applied to it. And the stored information in a memristor is non-volatile and also the resistance of a memristor can vary, through intermediate states, between high and low resistance states, by tuning the voltage and current. Therefore the memristor can be applied for analogue memory and/or learning device. Usually, memristive behavior is easily observed in the most transition metal oxide system, and it is explained by electrochemical migration motion of anion with electric field, electron scattering and joule heating. This paper reports the latest trends and issues of anion-based memristor.