With the expanding application of electronic devices in many areas, the requirements for memory devices are not only high speed and high density but also high flexibility. Flexible electronic devices are regarded as the next-generation electronic devices. Among the new memory devices, two-terminal resistive switching memory devices that have the structure of a polymer layer embedded with nanoparticles between two electrodes have attracted great attention. This article reviews the materials, electrical behavior, memory application and resistive switching mechanisms of two-terminal polymer:nanoparticle resistive switching memory devices. These devices can be classified into two categories in terms of the structure of the organic ligands capped on the nanoparticles. For the first type of device, nanoparticles capped with saturated organic ligands are embedded in the polymer. The resistive switches are insensitive to the interfaces between the polymer layer and the two electrodes. It is generally believed that the resistive switches are due to the charge trapping on the nanoparticles. In contrast, nanoparticles capped with conjugated organic ligands are exploited for the second type of device. The resistive switches are sensitive to the interfaces between the polymer layer and the two electrodes. The electric behavior of the devices is asymmetrical along the two polarities. The resistive switches are related to the charge transfer between the nanoparticles and electrode(s).