The statistical characterization of measurements arising from Internet traffic requires specific analysis and estimation techniques since the underlying traffic characteristics are often distributed with heavy tails. Here we provide a survey of fast and simple methods to detect the heaviness of tails and dependence in traffic data. We consider the dependence of both univariate and bivariate data. Important practical problems regarding the dependence between the transmission rate and file size or the time of transmission are dis-cussed as well. Finally, the recommended tools are illustrated by applications to real Web, TCP and video data.