The Navier-Stokes equation and its plasma analog indicate that the exchange of energy is produced by the quadratic term of the convective derivative. If one assumes that the energy exchange is local in wave number space, then it is possible to demonstrate that turbulent spectra take on the form of power laws. Since many observations of plasma wave spectra in the ionosphere and magnetosphere yield power laws, the turbulence hypothesis is an attractive interpretation. The least complex environment to study space plasma turbulence is the equatorial ionosphere. Here the Rayleigh-Taylor process injects energy as large coherent structures across a large region of k space, from 50 m to 100 km, and drift waves develop on the steep density gradients. In the most intense cases the drift waves cascade to short wavelengths. Hence the explanation of equatorial observations requires a hierarchy of processes. The high latitude ionosphere is not unstable to the Raleigh-Taylor process but nonetheless there is ample evidence for turbulent processes. The most compelling evidence is the existence of large scale density and electric field spatial irregularities throughout the auroral zone. Satellite evidence for the irregularities exists throughout the auroral zone and over the altitude range of 450 km to 13,000 km. The measurement techniques cover the wavelength range from 10 m to 800 m. In some cases the spectral index is the order of −5/3, implying a Kolmogorov process associated with fluid velocity shears (Kelvin-Helmholtz instability). In yet other cases the electric field fluctuations are associated with magnetic field fluctuations implying the existence of kinetic Alfvén waves. In other cases the index is much smaller, the order of −0.5, which does not agree with any of the local theories. In these cases better agreement may be obtained by considering nonlocal effects such as ionospheric coupling.