Machine learning and related statistical signal processing are expected to endow sensor networks with adaptive machine intelligence and greatly facilitate the Internet of Things. As such, architectures embedding adaptive and learning algorithms on-chip are oft-ignored by the design community and present a new set of design trade-offs. This review focuses on efficient implementation of mixed-signal matrix-vector multiplication as a central computational primitive enabling machine learning and statistical signal processing, with specific examples in spatial filtering for adaptive beamforming. We describe adaptive algorithms amenable for efficient implementation with such primitives in the presence of noise and analog variability. We also briefly highlight current trends in high-density integration in emerging memory device technologies and their use in high-dimensional adaptive computing.