Wind energy is poised to play a considerable role in the global transition to clean-energy technologies within the next few decades. Modern wind turbines, like aircraft and other aerodynamic structures, are typically designed with the assumption that the flows they encounter will be uniform and steady. However, atmospheric flows are highly unsteady, and systems operating within them must contend with gust disturbances that can lead to performance losses and structural damage. Therefore, the next generation of wind-energy systems requires physics-informed design principles that effectively account for and even leverage these unsteady flow phenomena for enhanced power generation, robustness, and operational longevity. Accordingly, this talk presents experimental and analytical efforts to characterize unsteady aerodynamics in wind-turbine contexts. First, we study the effects of unsteady streamwise motion on turbine performance, as recent work has suggested that these dynamics may enable time-averaged efficiencies that exceed the steady-flow Betz limit on turbine efficiency. The power production of and flow around a periodically surging wind turbine are thus investigated using experiments and analytical modeling, which suggest that floating offshore wind turbines could leverage unsteady surge motions for power-production gains of up to 6% over the stationary case. Additionally, field measurements in the wakes of full-scale vertical-axis wind turbines using artificial snow as tracer particles yield insights into the contributions of unsteady vortex dynamics to the performance of turbines in wind-farm arrays. These investigations provide the analytical and experimental foundations for future studies of unsteady atmospheric flows, which will lead to the development of principles and techniques for wind-farm siting, control, and optimization.