Adaptive channel equalization without resorting to a training sequence is often referred to as blind equalization. It can be used to improve data throughput by eliminating the training signal or to track the channel variations for fading channels. Blind equalization can be implemented directly by adjusting equalizer coefficients or indirectly by estimating first the channel parameters.^ For the direct equalization, this thesis studies the performance of the constant modulus algorithm (CMA), one of the most widely used and most successful methods. Connections between (nonblind) Wiener and (blind) CMA receivers are investigated. It is shown that the CMA receiver achieves almost the minimum mean square error (MMSE) performance. However, the existence of local minima may hinder its successful applications in practice. An analytical tool is also developed for the design of CMA receivers.^ For the blind channel estimation, this thesis investigates asymptotic performance and fundamental limitations of the class of blind channel estimators that use second-order statistics. Despite the potential to achieve fast convergence rate, the analysis shows that second-order methods have poor convergence rate for certain channels. To overcome this difficulty, a new algorithm which exploits subspace structure of channel modeling and cyclostationarity is proposed. Simulations show that the new algorithm significantly improves the channel estimation performance for multipath fading channels.