In this report, some hypothesis testing problems in distributed sensor networks are considered. Optimum data fusion rules are obtained when the decision rules at the detectors are known. The distributed hypothesis testing problem with a distributed data fusion is solved using the Bayesian as well as the Neyman-Pearson approach. The decentralized Neyman-Pearson hypothesis testing problem and the sequential hypothesis testing problem for a tandem topology network are investigated. The distributed sequential probability ratio test problem is also studied. In all these problems, optimal strategies at each site and at each time stage are obtained. Keywords include: Fusion, Surveillance, Remote Receivers, Detection, and Estimation. (r.h.)