This paper gives an overview of the methods and models used for the performance evaluation of asynchronous transfer mode (ATM)-based broad-band integrated services digital networks (B-ISDNs). Because these methods rely heavily upon stochastic processes theory, the relevant concepts from this field are succinctly recalled. The first main topic is traffic modeling. Because of the large impact upon the performance of B-ISDN systems, the concept of traffic burstiness is discussed and various definitions are given and compared. The most common stochastic traffic models are then discussed: on-off, Markov modulated sources, and Markovian process. The field of self-similar traffic is also reviewed. Another approach to source characterization is reviewed as well: bounded traffic models, which instead of a precise statistical description give a set of bounds on the cell generation process. The second main topic is the use of advanced queueing models for the performance evaluation of the ATM statistical multiplexer, the basic B-ISDN modeling concept underlying the design of switching elements, output buffers, rate adapters, etc. The three main solution methods for the statistical multiplexer are reviewed: matrix methods, generating function approach, and fluid flow approximation. This paper concludes with an overview of current topics in B-ISDN teletraffic research: connection admission control, buffer dimensioning, multiquality of service, cell discard schemes, rate-based flow control, per-virtual-connection queueing, and weighted fair queueing.