<p>Neuromorphic systems constructed from biomolecular materials offer rich dynamics and memory properties, enabling low-power, brain-like signal processing and computing. Unlike many neuromorphic devices, biomolecular materials and systems emulate the nanoscale architectures and physical mechanisms of biological synapses and neurons, which are responsible for the brain’s complex computing functions and energy efficiency. This article reviews our own efforts to develop a new class of neuromorphic hardware derived from voltage-responsive biomimetic membranes and membrane-bound ion channels. We review our published works, which integrated experiments, modeling, and simulations and demonstrated that biomimetic material systems can emulate key synaptic and neuronal behaviors through nonlinear dynamical changes in membrane ionic resistance and capacitance. Finally, we examine these models to identify sources of nonlinearities exhibited in their dynamic responses, and we briefly present our early efforts to understand how these unique forms of activity-dependent memory, nonlinearities, and plasticity mechanisms enhance signal processing and computing tasks.</p>