Many adaptive sensing and sensor management strategies seek to determine a sequence of sensor actions that successively optimizes an objective function. Frequently the goal is to adjust a sensor to best estimate a partially observed state variable, for example, the objective function may be the final mean-squared state estimation error. Information-driven sensor planning strategies adopt an objective function that measures the accumulation of information as defined by a suitable metric, such as Fisher information, Bhattacharyya affinity, or Kullback-Leibler divergence. These information measures are defined on the space of probability distributions of data acquired by the sensor, and there is a distribution in this space corresponding to each sensor configuration. Hence, sensor planning can be posed as a problem of optimally navigating over a statistical manifold of probability distributions. This information-geometric perspective presents new insights into adaptive sensing and sensor management.