Fluids trapped in small spaces feature prominently in science and technology, and understanding their properties is critical to progress in fields that range from cell biology to the engineering of nanoscale devices. Such “confined” fluids behave differently than bulk samples. Properties strongly affected by confinement include (i) how the particles pack together, (ii) how the thermodynamic state of the fluid is modified by squeezing or heating, and (iii) how (or how rapidly) the fluid mixes or flows. The first two have been reasonably well understood for some time, but a general rule for even qualitatively predicting the third has proven elusive. In this talk, we highlight how recent theory and molecular simulation have discovered quantitative links between the entropy (“randomness”) and the dynamics (“runniness”) of confined pure fluids and their mixtures. These links provide new physical insights and allow one to readily predict how confinement will impact the transport coefficients of bulk fluids.