We investigate how the sound field induced by an acoustic event evolves over space and time. The characteristics of its bidimensional Fourier spectrum are analyzed and spatio-temporal sampling results using an array of microphones are provided for different scenarios of interest. We then address the distributed compression problem using an information-theoretic point of view. In this context, optimal rate-distortion tradeoffs are derived for two scenarios of interest. A linear network setup is first considered, where a central base station aims at recovering with minimum distortion the signals recorded by an infinite line of microphones. A hearing aid problem is then studied, where two hearing devices exchange data over a rate-constrained wireless link in order to provide spatial noise reduction.