The character of seismic signals and noise is known on the basis of theoretical solutions of the elastic wave equation and from observations made at seismic stations and arrays. The design of these arrays depends on the correlation structure of the signals and noise, and on whether the goal is to separate mixed signals or to detect signals in noise., Advanced signal-processing techniques have been shown to be of practical importance in the mixed signal problem. Among techniques which have been developed beyond beamforming are three-dimensional frequency-wavenumber spectra, nonlinear three-component waveform filtering, maximum-likelihood processors using either a priori or measured signal and noise characteristics, and eigenvalue-eigenvector decompositions of mixed signals. Theory and examples will be given for each of these techniques.