Memristors have potential in high-efficiency information processing and synaptic function simulation due to their high density, low power consumption and continuously adjustable resistance. Zinc oxide is an ideal choice for memristor with high performance due to its various preparation methods, exciton stability and biocompatibility. Herein, the recent research progress of ZnO-based memristive device is reviewed, including memristive behaviors and mechanism, the cognitive functions of synapse simulated by analog-type memristor as well as functionality and applications. We first review the switching-type and corresponding memristive mechanism, including electronic memristors and optoelectronic memristors. Then, the cognitive functions of synapse including synaptic plasticity and learning experience are introduced. Moreover, we exhibit the applications of ZnO-based memristive device in logic operation, pattern recognition and multimodal in-sensor computing. Finally, we summarize the advantages/challenges of ZnO-based memristor and prospect the future development.