We consider spatial and spatio-temporal sigma-delta modulation structures for wideband signal acquisition with dense sensor arrays. Using closely arranged sensors, the array oversamples the signal in space and applies coarse quantization to each sensor output. A sigma-delta structure propagates quantization noise between sensors to shape the noise in space, just as a time-domain sigma-delta converter shapes noise in frequency. The spatially shaped noise is then filtered by a delay- and-sum beamformer. In this work, we also introduce higher-order sigma-delta structures and hybrid space-time architectures that can achieve greater noise shaping in both space and time. The coarsely quantized sigma-delta structure can be used to build high-resolution arrays with lower power and complexity.