  Turbulence is a key element of the dynamics of astrophysical fluids,
including those of interstellar medium, clusters of galaxies and circumstellar
regions. Turbulent motions induce Doppler shifts of observable emission and
absorption lines. In the review we discuss new techniques that relate the
spectra of underlying velocity turbulence and spectra of Doppler-shifted lines.
In particular, the Velocity-Channel Analysis (VCA) makes use of the channel
maps, while the Velocity Coordinate Spectrum (VCS) utilizes the fluctuations
measured along the velocity axis of the Position-Position Velocity (PPV) data
cubes. Both techniques have solid foundations based on analytical calculations
as well as on numerical testings. Among the two the VCS, which has been
developed quite recently, has two advantages. First of all, it is applicable to
turbulent volumes that are not spatially resolved. Second, it can be used with
absorption lines that do not provide good spatial sampling of different lags
over the image of turbulent object. In fact, numerical testing shows that
measurements of Doppler shifted absorption lines over a few directions is
sufficient for a reliable recovering of the underlying spectrum of the
turbulence. Our comparison of the VCA and the VCS with a more traditional
technique of Velocity Centroids, shows that the former two techniques recover
reliably the spectra of supersonic turbulence, while the Velocity Centroids may
have advantages for studying subsonic turbulence. In parallel with theoretical
and numerical work on the VCA and the VCS, the techniques have been applied to
spectroscopic observations. We discuss results on astrophysical turbulence
obtained with the VCA and the VCS.
