||Adaptive filtering is one of the most important techniques in signal processing for tracking the status of any time-varying system responses. With this property, adaptive filtering techniques have been widely used for channel estimation and equalization for several decades. In adaptive filtering algorithms, the new channel estimator or equalizer are usually updated based on the past results and the new incoming signals. The computational complexity and performance of this kind of recursive processes usually can be improved using the iterative techniques. In this thesis, I have proposed a set of novel iterative algorithms to estimate and/or equalize finite impulse response (FIR) single-input single-output (SISO), single-input multi-output (SIMO), and multi-input multi-output (MIMO) systems. An iterative channel estimation algorithm based on input and output signal correlation is proposed which is shown to be robust to instantaneous strong dis-turbance as well as time-varying correlative noise. This algorithm extended the cost function of the traditional RLS algorithm in correlation domain, such that the squared differences of the correlation function of the transmitted and received signals are considered in the adaptation. The channel adaptation performance is shown to be improved by smoothing the time-varying effects of the disturbance. The correlation-based iterative algorithm is a second-order statistics (SOS) based algorithm. I further extend this SOS algorithm from a non-blind SISO channel estimation to a blind SIMO channel estimation problem. An iterative subspace tracking algorithm is proposed. This algorithm eliminates the compu-tational intensiveness of eigenvalue decomposition process for each channel esti-mated by a least-mean-squares-alike subspace tracking algorithm. The simulation results showed that, compared to the traditional subspace method given in , the proposed algorithm, not only reduces the computational complexity, but also provides a comparable accuracy to that of the method in . The simulation results also show that the accuracy of the estimation can be further enhanced by adjusting the observation window size N in the adaptation algorithm. This allows the trade-off between the computation complexity and the equalization performance. Due to the spectral efficiency, I have proposed a blind equalizer for a spectral efficient block based FIR space-time precoder-equalizer system. In this design, MIMO frequency selective fading channels were considered. The proposed al-gorithm provides a blind equalizer for any FIR space-time precoder-equalizer system which has minimal number of transmit redundancy. This algorithm can be considered as a generic algorithm for providing the blind equalization for all the FIR block based transmitters, such as OFDM-VBLAST and trailing zero transmission. Apart from SOS based iterative algorithm, an higher-order statis-tics (HOS) based iterative blind channel equalization algorithm is investigated. This algorithm extracts the channel information from the HOS of the received signal. Since theoretically, the HOS will not be affected by the Gaussian signal, the proposed blind equalization algorithm is robust towards the additive Gaus-sian channel noise. The simulation results shows that the proposed algorithm has fast convergency rate and has good bit error rate (BER) performance at low signal-to-noise ratio (SNR) regime. Simulation results are presented in this dissertation to demonstrate the effec-tiveness and computational efficiency for all proposed iterative algorithms.