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In this thesis we explore applications of information theory to gene regulatory systems. Considering molecular recognition as an abstract communication channel, we are led to explore several biological problems in transcriptional regulation from an informational point of view. In particular, we study design principles for transcription factor binding motifs using protein-DNA coevolutionary models, maximum entropy methods for motif statistics, and exact sampling strategies for hybrid biophysical / evolutionary simulations. In Chapter 1 we review the necessary background and equip ourselves with a common stock of concepts from molecular biology and information theory. In Chapter 2 we present ESTReMo, a hybrid biophysical / evolutionary model of transcriptional regulation in which a DNA-binding domain and its cognate binding sites are co-evolved in silico. Simulating the behavior of the system over the cellular timescale and selecting its desired behavior over the evolutionary timescale, we provide a general framework for the exploration of hypothesized design principles of transcriptional regulation. For example, we confirm and generalize an argument relating the information content of a binding motif to its target occupancy, and find that active selection of pseudosites can serve to modulate occupancy. In Chapter 3 we consider a problem raised in the previous chapter: how can one determine whether a certain observed function of a binding motif is statistically unusual? Put another way, what is the correct null hypothesis for gapless alignments? To answer this question we develop two distributions over the space of binding motifs of given dimensions which can serve in this role. The first is a MaxEnt distribution over the space of motifs of given dimensions, subject to mean information content, and the second is a truncated uniform distribution over all motifs having information content within a specified interval. With efficient sampling algorithms for these distributions in hand, we show that both prokaryotic and eukaryotic binding motifs tend to exhibit larger informational Gini coefficients than would be expected by chance, and that this feature can be used to distinguish true binding motifs from false positives with matching information content. In Chapter 4 we yoke together information theory, biophysics and evolutionary biology in order to consider the problem of optimal molecular recognition strategies in binding motifs. Comparing linear models to those that incorporate pairwise correlations in a broad collection of prokaryotic and eukaryotic motifs and subjecting them to formal model comparison, we find that while simple linear models suffice for a large majority, most still contain a greater amount of pairwise mutual information content than would be expected by chance. In Chapter 5 we take stock and indicate some directions for future research.