An overview of distributed compression and estimation using wireless sensor networks (WSNs) in which the main design goals are performance, bandwidth efficiency, scalability, and robustness to changes in the network or environment is given. First, deterministic parameter estimators are pursued and intertwining tasks of quantization are studied in low signal-to-noise ratio (SNR) situations where the noise standard deviation is in the order of the parameter's dynamic range and universal estimation where the sensor data and noise model are known. It is shown that in the low SNR regime, universal distributed estimators not only exist but also achieve performance close to that of estimators based on the original observations. The techniques and basic results that are derived for the parameter estimation paradigms are also extended to more general and practical signal models. A Bayesian estimation framework is laid out along with an application to the state estimation of dynamical stochastic processes.