Compressive sensing (CS) in acoustics has received significant attention in the last decade, and thus motivates this special issue. CS emerged from the signal processing and applied math community and has since generated compelling results in acoustics. This special issue primarily addresses the acoustics CS topics of compressive beamforming and holography. For a sound field observed on a sensor array, CS reconstructs the direction of arrival of multiple sources using a sparsity constraint. Similarly, in holography a sparsity constraint gives improved sound field reconstruction over conventional ℓ2-regularization. Other topics in this issue include sparse array configurations (as co-arrays) and sparse sensing in acoustic communication.