In a recent article in APS News, John Hopfield, one of the founders of what has now become quantitative and systems biology, has defined physics as "The idea ... that the world is understandable." As a physicist working on biological problems, I pursue this understanding as the ultimate goal. Unfortunately, even for the simplest cellular networks, understanding their function is often obscured behind long and incomplete part lists of interaction partners, wiring diagrams, and differential equations. In this talk, I will describe how ideas of statistical physics and information theory allow us to make small steps towards formulation of and answers to questions like: What are the signal processing capabilities of stochastic biochemical networks? Which functions can they perform? How important is stochasticity? How can we understand network dynamics without microscopic simulations? While addressing these questions, I will also show examples of cross-fertilization between physics and systems biology: on the one hand, physics will suggest tools for faster simulation and deeper understanding of the networks dynamics, and, on the other, study of a biological problem will show an unexpected and illuminating connection between seemingly unrelated areas of theoretical physics.