Many researchers have discussed the effects of heavy-tailedness in network traffic patterns and shown that Internet traffic flows exhibit characteristics of self-similarity that can be explained by the heavy-tailedness of the various distributions involved. Self-similarity and heavy-tailedness are of great importance for network capacity planning purposes in which researchers are interested in developing analytical methods for analysing traffic characteristics. Designers of computing and telecommunication systems are increasingly interested in employing heavy-tailed distributions to generate workloads for use in simulation - although simulations employing such workloads may show unusual characteristics. Congested Internet situations, where TCP/IP buffers start to fill, show long-range dependent (LRD) self-similar chaotic behaviour. Such chaotic behaviour has been found to be present in Internet traffic by many researchers. In this context, the 'Hurst exponent', H, is used as a measure of the degree of long-range dependence. Having a reliable estimator can yield a good insight into traffic behaviour and may eventually lead to improved traffic engineering. In this paper, we describe some of the most useful mechanisms for estimating the tail index of Internet traffic, particularly for distributions having the power law observed in different contexts, and also the performance of the estimators for measuring the intensity of LRD traffic in terms of their accuracy and reliability.