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In this paper, we present an overview of recent work on the applications of Markov Chain Monte Carlo (MCMC) techniques to both multiple-input and multiple-output (MIMO) detection and channel equalization. In the setting of MIMO detection, we have shown that, even for very large antenna systems with high spectral efficiencies of 24 bits/channel use (8 transmit and 8 receive antennas with 64 QAM modulation), the MCMC MIMO detector can bring us within 2 dB of the channel capacity with a greatly reduced complexity compared to several versions of sphere decoding based detectors. For frequency selective channels, we demonstrate that MCMC-based equalizers yield excellent performance even for severe inter-symbol-interference (ISI) channels. The MCMC equalizer achieves significant performance gain over minimum mean square error (MMSE) linear equalizer and performs closely to the optimal maximum a posteriori probability (MAP) equalizer. We will also discuss new approaches that effectively alleviate the well-known high SNR problems in existing MCMC detectors.