Biological memory is the ability to develop, retain, and retrieve information over time. Currently, it is widely accepted that memories are stored in synapses (i.e., connections between brain cells throughout the brain) through a process known as synaptic plasticity, which leads to either long-term potentiation (LTP) or long-term depression (LTD). However, the strengthening (LTP) and weakening (LTD) of synapses involve post-translational modifications to neural networks requiring de novo gene expression, a lengthy and energetically expensive process. Recently, we observed that lipid bilayers in the absence of peptides/proteins are capable of LTP, not unlike what has been observed in mammals and birds. As such, this finding has prompted us to postulate that the lipid bilayer provides a good model for understanding the molecular basis of biological memory. In this article, we discuss the status, challenges, and opportunities of neuronal plasma membranes as structures for biological memory and learning, therapeutic targets for various brain disorders, and platforms for neural network developments.