Abstract: As promissing nonlinear dynamic electronic devices with widespread applications in computer data storage and neuromorphic implementations,memristor (also called "memory resistor"),which is a fourth circuit element with its effects predating the resistor,capacitor and inductor,has attracted tremendous attention in both materials science and condensed-matter physics since it was originally envisioned in 1971 by circuit theorist Leon Chua from UC-Berkley.Like the synapses of biological brains,memristors,which can learn from earlier impulses,combine the functions of memory and logic.In this review,we introduce the recent progress in the synthesis and biological synaptic mimicking of polymer memoristive materials.By using various pre-and postsynaptic spikes,the fundamental synaptic functions of short-term/long-term plasticity (STP/LTP),spike-timing dependent-plasticity (STDP),spike-rate dependent plasticity (SRDP) and "learning-memory-forget" experience can be mimicked in a polymer memoritive system.A larger number of experimental results have demonstrated that some important factors,including charge transfer and transport in materials,weak interaction between molecules,molecular structures and aggregation state structures of materials,microstructure of thin film,and electrical transport properties as well,have significant impact on the memristive switching performance of the resultant materials.