Systems where data is collected using arrays of sensors will usually contain a beamformer. When the number of active channels in the sensor array is large, as it often is in imaging systems like sonar and medical ultrasound, the beamformer can be both physically large and expensive. To counteract one or both of these unwanted effects, several compact beamforming solutions have been suggested. Delta-sigma based beamforming is one such technique, where 1-bit delta-sigma A/D converters are used to digitize the sensor data. In this thesis, several topics are considered. First, similarities between the acoustic applications microphone arrays, sonars and medical ultrasound imaging with respect to digital beamforming are considered. A generic digital acoustic beamformer is specified based on these similarities. A novel method for achieving distortion-free dynamic focusing in compact delta-sigma beamformers is presented. Delta-sigma beamforming applied to adaptive (Griffiths-Jim-based) beamformers is investigated with respect to compactness and effectiveness.