Allan variance (AVAR) was first introduced more than 40 years ago as an estimator of the stability of frequency standards, and now it is actively used for investigations of time series in astronomy, geodesy and geodynamics. This method allows one to explore effectively the noise characteristics for various data, such as variations of station and source coordinates, etc. Moreover, this technique can be used to investigate the spectral and fractal structure of the noise in measured data. To process unevenly weighted and multidimensional data, which are usual for many astronomy and geodesy applications, we propose AVAR modifications. We give a brief overview of the use of classical and modified AVAR method in astronomy and geodynamics.