To understand how bacteria adapt to hostile environments we need to understand the complex networks that process information and control gene-expression programs in response to stress. These complex networks called stress-response networks are a mesh of interconnected components that contain certain conserved structural elements such as feedback loops. This work aims to identify design principles that relate network structural elements to functional requirements in stress response networks using two known bacterial systems. First, we investigate dynamical properties of the Mycobacterium tuberculosis network that is responds to surface stress. In this network transcriptional master regulators MprAB two-component system (TCS) and alternative sigma factor sigma-E mutually activate each other creating positive feedback loops. In this project we build on previous mathematical models that predict bistability, and as a consequence hysteresis, in the network due to presence of positive feedback loops. Experimental observations confirm hysteresis but reveal surprisingly rapid response to stress, uncharacteristic of a bistable network. We seek to reconcile this seemingly discrepant experimental observations using a mathematical model of the known surface stress response network, but discover a trade-off between hysteresis and speed of response to stress. To resolve this trade-off we hypothesize a novel mechanism of activation of the MprAB TCS. Our new models of the stress-response network fit experimental observations, thereby resolving the trade-off. Follow-up experiments perturbing this hypothesized mechanism are consistent with predictions from our models. Thus, we show that synergistic use of experiments and modeling can improve our understanding of stress-response in clinically relevant bacterial species. In the second project, we investigate the E. coli network centered around the PhoPQ TCS which senses low extracellular Mg2+. Experiments indicate that the output of PhoPQ is relatively invariant to overexpression of the two components. While this is consistent with a model of the TCS, a later discovered negative feedback loop limiting PhoPQ activity raises questions about the results. Here we propose a mechanism that allows for invariance of output to PhoPQ overexpression despite the negative feedback loop. While dynamical properties of PhoPQ TCS have been published extensively, the role played by the overlaid positive and negative feedback loops in shaping the observed behavior has not been well understood. We show that the negative feedback leads to a plateau in steady state expression of genes in the PhoPQ regulon even as magnesium concentration decreases. We also describe how positive feedback is activated only when magnesium concentration decreases to growth-limiting levels. This resultant dose-response activation of PhoPQ in two phases is explained by a detailed model of PhoPQ hypothesizing a specific role played by MgrB. Further, we also find that this overlaid feedback loop structure enables cells to be sensitive to a wide range of magnesium concentrations. Finally, in a pivot from stress-response networks found in wild-type organisms, we investigate unexpected behavior of synthetic circuits designed to control gene expression noise independent of the mean. We build deterministic models to understand mechanisms that exploit positive feedback to yield ultrasensitivity and high cell-to-cell variance in gene expression. Stochastic models of the circuit accurately explain experimentally observed mean and noise properties, confirming our proposed mechanisms. Structural features like positive and negative feedback loops are common to a wide range of biological networks. Using mathematical modeling, we extract design principles of stress-response networks featuring feedback loops. The design principles identified in these studies should be widely applicable.