Before 2011, the Crab Nebula was considered to be a steady source of gamma-ray emission. Since then, rapid and powerful modulations of its gamma-ray flux have been observed by Fermi-LAT and/or AGILE about once per year. These events pose a major theoretical challenge, as they are at odds with stochastic (Fermi-type) particle acceleration theories, and would require magnetic energy densities well above those believed to characterize nebular plasma. In this talk I will discuss how the flares can be interpreted as evidence of turbulence in the pulsar's electromagnetic outflow, rather than of explosive magnetic reconnection events, which is the current paradigm. This interpretation requires a revision to conventional thinking about dissipation of electromagnetic energy in the pulsar wind, and also derives from recent advances in the theory of decaying magnetic turbulence.