In this paper, sensor network scenarios are considered where the underlying signals of interest exhibit a degree of sparsity, which means that in an appropriate basis, they can be expressed in terms of a small number of nonzero coefficients. Following the emerging theory of compressive sensing (CS), an overall architecture is considered where the sensors acquire potentially noisy projections of the data, and the underlying sparsity is exploited to recover useful information about the signals of interest, which will be referred to as distributed sensor perception. First, we discuss the question of which projections of the data should be acquired, and how many of them. Then, we discuss how to take advantage of possible joint sparsity of the signals acquired by multiple sensors, and show how this can further improve the inference of the events from the sensor network. Two practical sensor applications are demonstrated, namely, distributed wearable action recognition using low-power motion sensors and distributed object recognition using high-power camera sensors. Experimental data support the utility of the CS framework in distributed sensor perception.