New adaptive, iterative approaches to the decoding of block Turbo codes and multilevel codes are developed. Block Turbo codes are considered as they can readily provide high data rates, low decoding complexity and good performance. Multilevel codes are considered as they provide a moderate complexity approach to a high complexity code and can provide codes with good bandwidth efficiency. The work develops two adaptive sub-optimal soft output decoding algorithms for block Turbo codes. One is based on approximation and the other on the distance properties of the component codes. They can be used with different codes, modulation schemes, channel conditions and in different applications without modification. Both approaches provide improved performance compared to previous approaches on the additive white Gaussian noise (AWGN) channel. The approximation based adaptive algorithm is also investigated on the uncorrelated Rayleigh fiat fading channel and is shown to improve performance over previous approaches. Multilevel codes are typically decoded using a multistage decoder (MSD) for complexity reasons. Each level passes hard decisions to subsequent levels. If the approximation based adaptive algorithm is used to decode component codes in a traditional MSD it improves performance significantly. Performance can be improved further by passing reliability (extrinsic) information to all previous and subsequent levels using an iterative MSD. A new iterative multistage decoding algorithm for multilevel codes is developed by treating the extrinsic information as a Gaussian random variable. If the adaptive algorithms are used in conjunction with iterative multistage decoding on the AWGN channel, then a significant improvement in performance is obtained compared to results using a traditional MSD.