A number of CDMA receivers have been proposed that cover the whole spectrum of performance/complexity from the simple matched filter to the optimal Viterbi (1995) processor. Adaptive solutions, in particular, have the potential of providing the anticipated multiuser detection (MD) performance gains with a complexity that would be manageable for third generation systems. Our goal, in this article, is to provide an overview of previous work in MD with an emphasis on adaptive methods. We start with (suboptimal) linear receivers and discuss the data-aided MMSE receiver. Blind (nondata-aided) implementations are also reviewed together with techniques that can mitigate possible multipath effects and channel dispersion. In anticipation of those developments, appropriate discrete-time (chip rate) CDMA models are reviewed, which incorporate asynchronism and channel dispersion. For systems with large spreading factors, the convergence and tracking properties of conventional adaptive filters may be inadequate due to the large number of coefficients which must be estimated. In this context, reduced rank adaptive filtering is discussed. In this approach, the number of parameters is reduced by restricting the receiver tap vector to belong to a carefully chosen subspace. In this way the number of coefficients to be estimated is significantly reduced with minimal performance loss.