In recent years, increasing attention has been paid to application of resistor memory devices based on organic materials. They have been developed and studied because of several advantages, such as their low cost fabrication, flexible device structure, three-dimensional stacking capability, the possibility of modulating their properties through molecular design and chemical synthesis, etc. In this chapter, an overview of the development of resistor memory based on organic and polymeric materials is given in five sections covering the basics of resistor memory devices, materials, and a discussion of their underlying switching mechanisms. In addition, some of the recent studies on the applications of resistor memory devices will be presented in the final section.