Similar to other renewable energy sources, wind energy is characterized by a low power density. Hence, for wind energy to make considerable contributions to the world's overall energy supply, large wind farms (on- and offshore) consisting of arrays of ever larger wind turbines are being envisioned and built. From a fluid mechanics perspective, wind farms encompass turbulent flow phenomena occurring at many spatial and temporal scales. Of particular interest to understanding mean power extraction and fluctuations in wind farms are the scales ranging from 1 to 10 m that comprise the wakes behind individual wind turbines, to motions reaching 100 m to kilometers in scale, inherently associated with the atmospheric boundary layer. In this review, we summarize current understanding of these flow phenomena (particularly mean and second-order statistics) through field studies, wind tunnel experiments, large-eddy simulations, and analytical modeling, emphasizing the most relevant features for wind farm design and operation.