As wireless communication systems continue to push the limits of energy and spectral efficiency, increased demands are placed on the capabilities of the receiver. At the same time, the computational resources available for processing received signals will continue to grow. This opens the door for iterative algorithms to play an increasing role in the next generation of communication receivers. In the context of receivers, the goal of iterative probabilistic processing is to approximate maximum a posteriori (MAP) symbol-by-symbol detection of the information bits and estimation of the unknown channel or signal parameters. The sum-product algorithm is capable of efficiently approximating the marginal posterior probabilities desired for MAP detection and provides a unifying framework for the development of iterative receiver algorithms. However, in some applications the sum-product algorithm is computationally infeasible. Specifically, this is the case when both continuous and discrete parameters are present within the model. Also, the complexity of the sum-product algorithm is exponential in the number of variables connected to a particular factor node and can be prohibitive in multi-user and multi-antenna applications. In this dissertation we identify three key problems which can benefit from iterative probabilistic processing, but for which the sum-product algorithm is too complex. They are (1) joint synchronization and detection in multipath channels with emphasis on frame timing, (2) detection in co-channel interference and non-Gaussian noise, and (3) joint channel estimation and multi-signal detection. This dissertation presents the advances we have made in iterative probabilistic processing in order to tackle these problems. The motivation behind the work is to (a) compromise as little as possible on the performance that is achieved while limiting the computational complexity and (b) maintain good theoretical justification to the algorithms that are developed. / Ph. D.