Single cells sense their environment with remarkable precision. At the same time, cells have diverse mechanisms for communicating. How are sensing and communication connected? I will describe recent theoretical and experimental results that explore this question. First, I will show that to maximize sensory precision, it is often optimal for communicating cells to spread apart from each other, even though this behavior results in weaker communication. Then, I will argue that cells can use signaling feedback to enhance communication, and potentially sensory precision. This will lead to concrete connections between nonequilibrium cell signaling and equilibrium critical systems, allowing one to interpret experimental data from immune cells in the language of statistical physics.