As the fourth type of passive electronic device, memristor is considered to be a strong competitor of the next generation of nonvolatile memory and artificial synaptic device due to its simple structure, fast storage speed and high integration density. Currently, resistive, capacitive, and inductive sensors have clear principles, and are extensively investigated and widely applied, which are constructed based on the three types of passive electronic devices—resistor, capacitor, and inductor. However, the research of memristor based memristive sensor is still in the preliminary stage. In this paper, the properties, materials, mechanism and applications of memristor are introduced briefly. Based on the research of memristor in sensing field, the concept and definition of the memristive sensor are proposed. Then, the research progress on the sensing characteristics of physical quantity, chemical quantity and biological quantity by memristor is reviewed. Finally, the challenges and future prospects of memristive sensors are discussed, providing feasible directions for the future research of memristive sensor.