Statistical multiplexers play a central role in the design of high‐speed multiservice telecommunications networks. As network links reach capacities of terabits per second, the multiplexing of a large number variable rate voice, video and data sources on a common channel can achieve significant savings in the bandwidth consumed by each source. This resource sharing paradigm must be examined by considering the traffic characteristics, performance requirements and multiplexing system parameters. Traffic on broadband networks is characterized by complex features that include correlation over many time scales, significant dispersion about the mean rate, nonstationary variations in average rate and variance and in some cases deterministic fluctuations. These features render classical Poisson traffic based approaches to performance analysis inaccurate. This paper presents a overview of new traffic models and performance analysis techniques for statistical multiplexing systems. The application of renewal processes, Markov chains, time‐series models and self‐similar processes as traffic models are discussed. Analytic, computational and approximate performance analyses of statistical multiplexers are reviewed. The design of admission control algorithms for controlling statistical multiplexing performance using moment matching methods, fluid flow approximations, large‐deviation principles and effective bandwidth approximations are discussed.