The rates of many chemical processes are much slower than one might have predicted from molecular speeds.  Often that is because the process has to wait until the molecules have accumulated enough energy to climb over some reasonably high spots on their potential energy landscapes.  But in some kinds of glassy liquids, and even in some examples with ordinary liquids, the dynamics is still remarkably slow despite the fact that the potential energy barriers are not all that high.  Our research suggests that a better way to understand these examples of slow dynamics is to focus not on the barriers, but on the most efficient pathways that the molecules in the liquid can take through their potential energy landscapes.  From this perspective, the reason that dynamics slows down is because these most efficient pathways – the geodesics – have become long and convoluted.  This talk will describe how the calculation of geodesic molecular pathways allows us to study the unusual dynamics seen in both glass-forming liquids and liquid mixtures that exhibit preferential solvation.