  Magnetohydrodynamic (MHD) turbulence is a crucial component of the current
paradigms of star formation, dynamo theory, particle transport, magnetic
reconnection and evolution of structure in the interstellar medium (ISM) of
galaxies. Despite the importance of turbulence to astrophysical fluids, a full
theoretical framework based on solutions to the Navier-Stokes equations remains
intractable. Observations provide only limited line-of-sight information on
densities, temperatures, velocities and magnetic field strengths and therefore
directly measuring turbulence in the ISM is challenging. A statistical approach
has been of great utility in allowing comparisons of observations, simulations
and analytic predictions. In this review article we address the growing
importance of MHD turbulence in many fields of astrophysics and review
statistical diagnostics for studying interstellar and interplanetary
turbulence. In particular, we will review statistical diagnostics and machine
learning algorithms that have been developed for observational data sets in
order to obtain information about the turbulence cascade, fluid compressibility
(sonic Mach number), and magnetization of fluid (Alfv\'enic Mach number). These
techniques have often been tested on numerical simulations of MHD turbulence,
which may include the creation of synthetic observations, and are often
formulated on theoretical expectations for compressible magnetized turbulence.
We stress the use of multiple techniques, as this can provide a more accurate
indication of the turbulence parameters of interest. We conclude by describing
several open-source tools for the astrophysical community to use when dealing
with turbulence.
