The emergence of single-molecule (SM) fluorescence techniques has opened up a vast new toolbox for exploring the molecular basis of life. The ability to monitor individual biomolecules in real time enables complex, dynamic folding pathways to be interrogated without the averaging effect of ensemble measurements. In parallel, modern biology has been revolutionized by our emerging understanding of the many functions of RNA. In this comprehensive review, we survey SM fluorescence approaches and discuss how the application of these tools to RNA and RNA-containing macromolecular complexes in vitro has yielded significant insights into the underlying biology. Topics covered include the three-dimensional folding landscapes of a plethora of isolated RNA molecules, their assembly and interactions in RNA-protein complexes, and the relation of these properties to their biological functions. In all of these examples, the use of SM fluorescence methods has revealed critical information beyond the reach of ensemble averages.