Abstract: Latest progresses on some fundamental and important problems about information fusion in sensor networks are presented,including the multisensor distributed decision in the most general case in the sense of globally optimal fusion;the optimal dimension compression of the sensor observations or local estimates;the best linear unbiased estimation fusion formula and the efficient iterative algorithm;the distributed Kalman filtering fusion for the(multisensor) dynamic systems with cross-correlated sensor noises;and the fault-tolerant interval estimation fusion.These results are significant to the design and application of sensor networks.