In many distant speech acquisition scenarios, such as hands-free telephony or teleconferencing, the desired speech signal is corrupted by noise and reverberation. This degrades both the speech quality and intelligibility, making communication difficult or even impossible. Speech enhancement techniques seek to mitigate these effects and extract the desired speech signal. This objective is commonly achieved through the use of microphone arrays, which take advantage of the spatial properties of the sound field in order to reduce noise and reverberation. Spherical microphone arrays, where the microphones are arranged in a spherical configuration, usually mounted on a rigid baffle, are able to analyze the sound field in three dimensions; the captured sound field can then be efficiently described in the spherical harmonic domain (SHD). In this thesis, a number of novel spherical array processing algorithms are proposed, based in the SHD. In order to comprehensively evaluate these algorithms under a variety of conditions, a method is developed for simulating the acoustic impulse responses between a sound source and microphones positioned on a rigid spherical array placed in a reverberant environment. The performance of speech enhancement algorithms can often be improved by taking advantage of additional a priori information, obtained by estimating various acoustic parameters. Methods for estimating two such parameters, the direction of arrival (DOA) of a source (static or moving) and the signal-to-diffuse energy ratio, are introduced. Finally, the signals received by a microphone array can be filtered and summed by a beamformer. A tradeoff beamformer is proposed, which achieves a balance between speech distortion and noise reduction. The beamformer weights depend on the noise statistics, which cannot be directly observed and must be estimated. An estimation algorithm is developed for this purpose, exploiting the DOA estimates previously obtained to differentiate between desired and interfering coherent sources.