In this paper, research into several aspects of robot-enabled reconnaissance of random fields is reported. The work has two major components: the underlying theory of information acquisition in the exploration of unknown fields and the results of experiments on how humans use sensor-equipped robots to perform a simulated reconnaissance exercise. The theoretical framework reported herein extends work on robotic exploration that has been reported by ourselves and others. Several new figures of merit for evaluating exploration strategies are proposed and compared. Using concepts from differential topology and information theory, we develop the theoretical foundation of search strategies aimed at rapid discovery of topological features (locations of critical points and critical level sets) of a priori unknown differentiable fields. The theory enables study of efficient reconnaissance strategies in which the tradeoff between speed and accuracy can be understood. The proposed approach to rapid discovery of topological features has led in a natural way to the creation of parsimonious reconnaissance routines that do not rely on any prior knowledge of the environment. The design of topology-guided search protocols uses a mathematical framework that quantifies the relationship between what is discovered and what remains to be discovered. The quantification rests on an information theory inspired model whose properties allow us to treat search as a problem in optimal information acquisition. A central theme in this approach is that “conservative” and “aggressive” search strategies can be precisely defined, and search decisions regarding “exploration” versus “exploitation” choices are informed by the rate at which the information metric is changing. The paper goes on to describe a computer game that has been designed to simulate reconnaissance of unknown fields. Players carry out reconnaissance missions by choosing sequences of motion primitives from two families of control laws that enable mobile robots to either ascend/descend in gradient directions of the field or to map contours of constant field value. The strategies that emerge from the choices of motion sequences are classified in terms of the speed with which information is acquired, the fidelity with which the acquired information represents the entire field, and the extent to which all critical level sets have been approximated. The game thus records each player's performance in acquiring information about both the topology and geometry of the unknown fields that have been randomly generated.