Fine-tuned ion transport across nanoscale pores is key to many biological processes, including neurotransmission. Recent advances have enabled the confinement of water and ions to two dimensions, unveiling transport properties inaccessible at larger scales and triggering hopes of reproducing the ionic machinery of biological systems. Here we report experiments demonstrating the emergence of memory in the transport of aqueous electrolytes across (sub)nanoscale channels. We unveil two types of nanofluidic memristors depending on channel material and confinement, with memory ranging from minutes to hours. We explain how large time scales could emerge from interfacial processes such as ionic self-assembly or surface adsorption. Such behavior allowed us to implement Hebbian learning with nanofluidic systems. This result lays the foundation for biomimetic computations on aqueous electrolytic chips.