Chemists visualize chemical reactions as motion along one-dimensional "reaction coordinates" over free energy barriers. Various rate theories, such as transition state theory and the Kramers theory of diffusive barrier crossing, differ in their assumptions regarding the mathematical specifics of this motion. Direct experimental observation of the motion along reaction coordinates requires single-molecule experiments performed with unprecedented time resolution. Toward this goal, recent single-molecule studies achieved time resolution sufficient to catch biomolecules in the act of crossing free energy barriers as they fold, bind to their targets, or undergo other large structural changes, offering a window into the elusive reaction "mechanisms". This Perspective describes what we can learn (and what we have already learned) about barrier crossing dynamics through synergy of single-molecule experiments, theory, and molecular simulations. In particular, I will discuss how emerging experimental data can be used to answer several questions of principle. For example, is motion along the reaction coordinate diffusive, is there conformational memory, and is reduction to just one degree of freedom to represent the reaction mechanism justified? It turns out that these questions can be formulated as experimentally testable mathematical inequalities, and their application to experimental and simulated data has already led to a number of insights. I will also discuss open issues and current challenges in this fast evolving field of research.