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This paper provides an overview of distributed estimation-compression problems encountered with wireless sensor networks (WSN). A general formulation of distributed compression-estimation under rate constraints was introduced, pertinent signal processing algorithms were developed, and emerging tradeoffs were delineated from an information theoretic perspective. Specifically, we designed rate-constrained distributed estimators for various signal models with variable knowledge of the underlying data distributions. We proved theoretically, and corroborated with examples, that when the noise distributions are either completely known, partially known or completely unknown, distributed estimation is possible with minimal bandwidth requirements which can achieve the same order of mean square error (MSE) performance as the corresponding centralized clairvoyant estimators.