ABSTRACT The unique structural features of deoxyribonucleic acid (DNA) that are of considerable biological interest also make it a valuable engineering material. Perhaps the most useful property of DNA for molecular engineering is its ability to self-assemble into predictable, double helical secondary structures. These interactions are exploited to design a variety of DNA nanostructures, which can be organized into both discrete and periodic structures. This dissertation focuses on studying the dynamic behavior of DNA nanostructure recognition processes. The thermodynamics and kinetics of nanostructure binding are evaluated, with the intention of improving our ability to understand and control their assembly. Presented here are a series of studies toward this goal. First, multi-helical DNA nanostructures were used to investigate how the valency and arrangement of the connections between DNA nanostructures affect super-structure formation. The study revealed that both the number and the relative position of connections play a significant role in the stability of the final assembly. Next, several DNA nanostructures were designed to gain insight into how small changes to the nanostructure scaffolds, intended to vary their conformational flexibility, would affect their association equilibrium. This approach yielded quantitative information about the roles of enthalpy and entropy in the affinity of polyvalent DNA nanostructure interactions, which exhibit an intriguing compensating effect. Finally, a multi-helical DNA nanostructure was used as a model `chip' for the detection of a single stranded DNA target. The results revealed that the rate constant of hybridization is strongly dominated by a rate-limiting nucleation step.