  We discuss a long-standing problem of how turbulence can be studied using
observations of Doppler broadened emission and absorption lines. The focus of
the present review is on two new techniques, the Velocity-Channel Analysis
(VCA), which makes use of the channel maps, and the Velocity Coordinate
Spectrum (VCS), which utilizes the fluctuations measured along the velocity
axis of the Position-Position Velocity (PPV) data cubes. Both techniques have
solid theoretical foundations based on analytical calculations as well as on
numerical testings. Among the two the VCS, which has been developed quite
recently, has two unique features. 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 the turbulent object. In fact, recent studies show that measurements
of absorption line along less than 10 absorption directions are sufficient for
a reliable recovering of the underlying spectrum of the turbulence. Moreover,
both weak absorption lines and absorption lines in saturated regime can be
used, which extends the applicability of the technique. 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 be used only for studying subsonic
turbulence. We discuss spectra of astrophysical turbulence obtained with the
VCA and the VCS techniques.
