Massive multiuser (MU) multiple-input multiple-output (MIMO) promises significant improvements in spectral efficiency compared to small-scale MIMO. Typical massive MU-MIMO base-station (BS) designs rely on centralized linear data detectors and precoders which entail excessively high complexity, interconnect data rates, and chip input/output (I/O) bandwidth when executed on a single computing fabric. To resolve these complexity and bandwidth bottlenecks, we propose new decentralized algorithms for data detection and precoding that use coordinate descent. Our methods parallelize computations across multiple computing fabrics, while minimizing interconnect and I/O bandwidth. The proposed decentralized algorithms achieve near-optimal error-rate performance and multi-Gbps throughput at sub-1 ms latency when implemented on a multi-GPU cluster with half-precision floating-point arithmetic.