Tracking multiple moving objects in complex environments is a key objective of many robotic and aerospace surveillance systems. In the Bayesian multi-object tracking framework, noisy sensor measurements are assimilated over time to form probabilistic beliefs, namely probability densities, of the multi-object state by virtue of Bayes' rule. This dissertation shows that, using probabilistic beliefs and environmental feedback, intelligent sensors can also optimize the value of information gathered in real time by means of information-driven control. In particular, it is shown that in object tracking applications, sensor actions can be optimized based on the expected reduction in uncertainty or information gain estimated from probabilistic beliefs for future sensor measurements. When compared to traditional estimation problems, the problem of estimating the information value for multi-object surveillance is more challenging due to unknown object-measurement association and unknown object existence. The advent of random finite set (RFS) theory has provided a formalism for quantifying and estimating information gain in multi-object tracking problems. However, direct computation of many relevant RFS functions, including posterior density functions and predicted information gain functions, is often intractable and requires principled approximation. This dissertation presents new theory, approximations, and algorithms related to autonomous multi-sensor multi-object surveillance. A new approach is presented for systematically incorporating ambiguous inclusion/exclusion type evidence, such as the non-detection of an object within a known sensor field-of-view (FoV). The resulting state estimation problem is nonlinear and solved using a new Gaussian mixture approximation achieved through recursive component splitting.Based on this approximation, a novel Gaussian mixture Bernoulli filter for imprecise measurements is derived. The filter can accommodate "soft" data from human sources and is demonstrated in a tracking problem using only natural language statements as inputs. This dissertation further investigates the relationship between bounded FoVs and cardinality distributions for a representative selection of multi-object distributions. These new FoV cardinality distributions can be used for sensor planning, as is demonstrated through a problem involving a multi-Bernoulli process with up to one hundred potential objects. Finally, a new tractable approximation is presented for RFS expected information gain that is applicable to sensor control in multi-sensor multi-object search-while-tracking problems. Unlike existing RFS approaches, the approximation presented in this dissertation accounts for multiple measurement outcomes due to noise, missed detections, false alarms, and object appearance/disappearance. The effectiveness of the information-driven sensor control is demonstrated through a multi-vehicle search-while-tracking experiment using real video data from a remote optical sensor.