Cells are computational entities that process external signals through networks of interacting proteins and reconfigure their state via biochemical modifications of proteins and changes in gene expression. Despite progress in the understanding of signaling and gene regulation in biology, graph diagrams typically used as depictions of relationships only offer qualitative abstractions. New single-cell measurement technologies provide quantitatively precise measurements of hundreds of cellular components representing important biochemical functions. However, a major challenge in deciphering single-cell signaling data is developing computational methods that can handle the complexity, noise and bias in the measurements. I will describe algorithms that quantify the flow of information through signaling interactions and mathematically characterize relationships between signaling molecules, using statistical techniques to detect dependencies while mitigating the effect of noise. I will show how these algorithms can be utilized to characterize signaling relationships in immune cells, detect subtle differences between cell types, and predict differential responses to perturbation. Then, I will show how multidimensional extensions of these techniques can be used to track dynamic changes in the relatively unknown network driving the epithelial-to-mesenchymal (EMT) transition that occurs during cancer metastasis, with the goal of predicting drugs to halt the process. Finally, I will present current work on extending these ideas to transcriptomic data where both the dimensionality and sparsity of the data pose a greater challenge.