In this paper, we assess the progress that has been made in the field of memories employing organic-based molecular or polymer layers. Such technologies explore the use of low-cost "bottom-up" approaches (i.e. chemical synthesis, molecular self-assembly), and the behavior of devices is governed by the properties of specifically designed molecular and polymer organic species. In particular, we discuss capacitive-and resistive-based electrical storage behaviors, employing two-or three-terminal device architectures. It should be stated that, today, the field remains exploratory. The recent findings in the fields of organic-based molecular and polymer memories show that such technologies may have some features of interest to mainstream storage technologies within the next few decades, and on a shorter term address new markets (plastic electronics, flexible/wearable electronics.) that are not be fully covered by existing technologies. Nevertheless, great challenges in terms of device fabrication and integration still remain, and an extensive set of proof-of-concept experiments still needs to be provided. (C) 2011 Elsevier B. V. All rights reserved.