We take a theoretical approach to the problem of identification, or 'reverse engineering', of gene regulatory networks. Through a mathematical model of a gene regulatory network, we examine fundamental questions on the limits and achievability of network identification. We apply simplifying assumptions to construct an acyclic binary model, and we assume that the identification strategy is restricted to perturbing the network by gene expression assignments, followed by expression profile measurements at steady-state. Further, we assume the presence of side information, which we call sensitivity, that is likely to be present in actual gene networks. We show that with sensitivity side information and realistic topology assumptions we can identify the topology of acyclic binary networks using O(n) assignments and measurements, n being the number of genes in the network. Our work establishes a theoretical framework for examining an important technological problem where a number of significant questions remain open.