The demand for more efficient and faster memory structures is greater today than ever before. The efficiency of memory structures is measured in terms of storage capacity and the speed of functioning. However, the production cost of such configurations is the natural constraint on how much can be achieved. Organic memory devices (OMDs) provide an ideal solution, in being inexpensive, and at the same time promising high performance. However, all OMDs reported so far suffer from multiple drawbacks that render their industrial implementation premature. This article introduces the different types of OMDs, discusses the progress in this field over the last 9 years and invokes conundrums that scholars of this field are currently faced with, such as questions about the charging mechanism and stability of devices, contradictions in the published work and some future directions.