Turbulence is ubiquitous in astrophysical plasmas, but remains mysterious from a theoretical perspective. A major reason for this is intermittency, the inherent inhomogeneity of turbulence, which causes processes such as energy dissipation and particle acceleration to be highly localized in coherent structures. I will describe how the statistical analysis of coherent structures can give new insights into intermittency. This methodology will be applied to analyze dissipative current sheets in numerical simulations of driven magnetohydrodynamic turbulence. I will describe how the overall energy dissipation is partitioned among current sheets with different energy dissipation rates and characteristic scales (length, width, and thickness). The temporal properties of the current sheets and their scalings with Reynolds number will also be described. I will discuss possible space and astrophysical applications and implications of this work, including a comparison with the observed statistical properties of solar flares.