We study the problem of distributed detection, where a set of nodes is required to decide between two hypotheses based on available measurements. We seek fully distributed and adaptive implementations, where all nodes make individual real-time decisions by communicating with their immediate neighbors only, and no fusion center is necessary. The proposed distributed detection algorithms are based on diffusion strategies [C. G. Lopes and A. H. Sayed, “Diffusion Least-Mean Squares Over Adaptive Networks: Formulation and Performance Analysis,” IEEE Trans. Signal Process., vol. 56, no. 7, pp. 3122-3136, July 2008; F. S. Cattivelli and A. H. Sayed, “Diffusion LMS Strategies for Distributed Estimation,” IEEE Trans. Signal Process., vol. 58, no. 3, pp. 1035-1048, March 2010; F. S. Cattivelli, C. G. Lopes, and A. H. Sayed, “Diffusion Recursive Least-Squares for Distributed Estimation Over Adaptive Networks,” IEEE Trans. Signal Process., vol. 56, no. 5, pp. 1865-1877, May 2008] for distributed estimation. Diffusion detection schemes are attractive in the context of wireless and sensor networks due to their scalability, improved robustness to node and link failure as compared to centralized schemes, and their potential to save energy and communication resources. The proposed algorithms are inherently adaptive and can track changes in the active hypothesis. We analyze the performance of the proposed algorithms in terms of their probabilities of detection and false alarm, and provide simulation results comparing with other cooperation schemes, including centralized processing and the case where there is no cooperation. Finally, we apply the proposed algorithms to the problem of spectrum sensing in cognitive radios.