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Distance sensitivity is a locality concept that is useful for designing scalable wireless sensor network applications. In this paper, we formally define distance sensitivity and we highlight its different forms such as distance sensitive latency, error, rate, membership, and healing. We show how distance sensitivity allows the application requirements and the network specification to be stated (and reasoned about) purely in geometric terms. This paper also examines key aspects of the concept, namely sufficiency, decomposability, and robustness. Specifically, sufficiency involves consideration of whether distance sensitive properties are enough for meeting application requirements. Decomposability involves choosing properties of network layers/components so that together the distance sensitive network abstraction holds. And, robustness implies preservation of distance sensitivity in the presence of failures in the network, including both permanent and transient failures and even those that violate the density or geometric assumptions of the network. We illustrate these aspects via examples from our previous work, all in the context of a common case study, regarding the design of a distributed pursuer evader tracking application.