This thesis presents new structures and algorithms for multiuser detection and interference suppression in DS-CDMA systems. Structures based on recurrent neural networks are investigated for decision feedback receivers and adaptive algorithms are developed for combatting multiple access interference and intersymbol interference. New algorithms based on the minimization of the bit error rate are examined and generalized for detection schemes with interference cancellation. For situations where a training sequence is not available, a new blind criterion, based on the constant modulus cost function with linear constraints is considered. Based on this novel criterion, blind adaptive algorithms are used for estimating the parameters of linear receivers and the channel. New blind adaptive mechanisms for adjusting the step size of stochastic gradient algorithms, using the constrained minimum variance criterion, are also presented for estimating the parameters of linear receivers and the channel. Based on constrained minimum variance and constrained constant modulus criteria, the blind design of decision feedback structures is considered and blind adaptive algorithms are derived. A new successive interference cancellation scheme using the concept of arbitration is proposed and incorporated within a decision feedback structure for uplink scenarios. Then, the new interference cancellation scheme is combined with an iterative structure that employs multiple stages, resulting in improved receiver estimates and providing uniform performance over the users. Finally, novel reduced-rank receiver structures, based on interpolated FIR filters with time-varying interpolators, are presented and blind and supervised adaptive algorithms are developed for this new scheme.