A basic mechanism for storing data in memory cells is to record changes in electronic charges, material phases, resistivities, magnetic properties, and so forth. The change in electronic charge has been widely used in the majority of mass-produced memories, such as dynamic random-access memory (DRAM), static random-access memory (SRAM), NOR Flash, and NAND Flash. Other emerging memories have collected widespread attention for acquiring extra advantages which cannot be achieved using the change in electronic charge. Many years of studies have told us that reliability problems are critically important in the development of both conventional and emerging memories, in order to improve the product yield. However, the topics related to these problems are too wide to cover in these limited pages. In this review chapter, we address several interesting examples of trap-related problems in dielectrics for use in various memory cells. For engineering purposes, it is very important to grasp the relation of the achieved physical intuitions and electronic characteristics of dielectrics.