Abstract : On length scales larger than the ion gyroradius, the turbulence in a plasma with a strong mean magnetic field may be modelled using the equations of reduced magnetohydrodynamics, which describe the evolution of Alfvenic fluctuations propagating up and down the magnetic field. This (strongly nonlinear) turbulence is (i) anisotropic with respect to the direction of the local mean magnetic field - a steeper spectral index (for example) in the parallel direction compared to the perpendicular. (ii) "aligned" - vector fluctuations in the fields in the perpendicular plane point in the same direction to within a small angle. (iii) highly intermittent - the shape of the probability distributions of many (but not all!) turbulent quantities depends on scale in a non-trivial way. I will discuss the work we have performed connecting these phenomena, and the resulting statistical model for the Alfvenic turbulence we have developed.