Gene expressions are essentially regulated by transcription factor-DNA interactions. Many transcription factors bind to DNA with remarkably low specificity, so that the functional binding sites have to compete with an enormous number of non-functional "decoy" sites. The functional roles that decoy sites play in regulating gene expressions are still largely unknown. In this thesis, I utilized mathematical modeling approaches to elucidate the functional roles of transcription factor decoys in gene regulation across different scales, using the biologically-important NFkB/IkB signaling network as a real example. My study showed that with biologically-relevant binding/unbinding kinetic rates, transcription factor decoys are able to modulate both the time-scales and the amplitude of the systems-level dynamics of gene regulatory networks. Also by means of stochastic models and Monte Carlo simulations, I was able to uncover the mechanistic principles of how decoys modulate stochastic dynamics of gene regulatory networks, given that the binding affinities of decoys are widely distributed according to experiments. My study challenges the conventional bioinformatics principle of protein-DNA interactions and provide significant scientific insights in single cell analysis. The multi-scale mathematical models developed from this thesis are also capable of providing quantitative guidance for therapeutic applications of artificial decoys for NFkB-related diseases.