Energy dissipation in turbulent plasmas is highly intermittent, which has widespread consequences for laboratory, space, and astrophysical systems. In this thesis, the intermittency of energy dissipation in numerical simulations of driven magnetohydrodynamic turbulence is investigated. A methodology is developed for identifying and characterizing intermittent dissipative structures and spatiotemporal processes. A statistical analysis is then performed on the resulting population. At any given time, the energy dissipation of the system is found to be evenly spread among current sheets with energy dissipation rates, lengths, and widths in the inertial range, and thicknesses localized within the dissipation range. These current sheets are involved in complex, time-asymmetric spatiotemporal processes that have durations up to several large eddy turnover times. The largest and most intense dissipative processes dominate the energy dissipation of the system. The scalings of the statistical properties with Reynolds number are estimated. These results are then compared with the observed statistical properties of solar flares.