Multiuser detection strategies are derived and analyzed for several signal detection problems arising in Code-Division Multiple-Access channels. Modulation schemes which lend themselves to coherent and noncoherent demodulation are considered. For coherent communication, a suboptimum multistage detection strategy based on successive multiple-access interference rejection is proposed for both synchronous and asynchronous Gaussian CDMA channels. The resulting multistage detectors process the sufficient statistics via a nonlinear multistage decision algorithm. An efficient, fixed decoding delay implementation of the multistage detector for the asynchronous channel is obtained and is shown to require a computational and storage complexity per binary decision which is linear in the number of users K. The multistage detector therefore contrasts the optimum demodulator, which is based on a dynamic programming algorithm; has a variable decoding delay; and a software complexity which is exponential in K. Performance analysis of the multistage detector is characterized in terms of bit-error probability. A comparative error probability study is undertaken between the conventional, optimum and the multistage detectors along with the decorrelating suboptimum detectors. Results obtained here indicate that significant improvements over the conventional single-user detector in bandwidth efficiency and near-far immunity are afforded by the multistage and decorrelating detectors. The multistage detector is particularly well suited for the demodulation of signals of widely dissimilar energies, corresponding to near-far scenarios. The noncoherent multiuser detection problem is studied for the synchronous CDMA channel where the modulation scheme considered is differential phase-shift keying. A class of quadratic detectors is defined with the objective of chosing the optimal quadratic detector. Asymptotic efficiency is considered as the performance measure of interest. It is equivalent to error probability in the low background noise region and quantifies performance loss due to presence of interfering signals. Since the receiver does not attempt to estimate signal energies and phases in this noncoherent system, the optimal detector is chosen as the one which optimizes the worst-case asymptotic efficiency over interfering signal uncertainties. This minimax approach yields an optimal detector, the bit-error probability of which is invariant to interfering signal uncertainties, thereby alleviating the near-far problem associated with the conventional single-user detection scheme.