We present TurbuStat (v1.0): a Python package for computing turbulence statistics in spectral-line data cubes. TurbuStat includes implementations of fourteen methods for recovering turbulent properties from observational data. Additional features of the software include: distance metrics for comparing two data sets; a segmented linear model for fitting lines with a break-point; a two-dimensional elliptical power-law model; multi-core fast-fourier-transform support; a suite for producing simulated observations of fractional Brownian Motion fields, including two-dimensional images and optically-thin HI data cubes; and functions for creating realistic world coordinate system information for synthetic observations. This paper summarizes the TurbuStat package and provides representative examples using several different methods. TurbuStat is an open-source package and we welcome community feedback and contributions.