Liquids are usually described within classical physics, whereas solids require the tools of quantum mechanics. I will show how in nanoscale systems this distinction no longer holds. At these scales, liquid flows may in fact exhibit quantum effects as they interact with electrons in the solid walls. I will first discuss the quantum friction phenomenon, where charge fluctuations in the liquid interact with electronic excitations in the solid to produce a hydrodynamic friction force. Using many-body quantum theory, we predict that this effect is particularly important for water flowing on carbon-based materials, and we obtain experimental evidence of the underlying mechanism from pump-probe terahertz spectroscopy. I will then show how the theory can be pushed one step further to describe hydrodynamic Coulomb drag – the generation of electric current by a liquid in the solid along which it flows. This phenomenon involves a subtle interplay of electrostatic and electron-phonon interactions, and suggests strategies for designing materials with low hydrodynamic friction.