Biochemical reactions constitute the cell's computing language. Thirty years ago, Berg and Purcell showed that bacterial chemotaxis, where a single-celled organism responds to small changes in the concentration of chemicals outside the cell, is limited directly by molecule counting noise and that aspects of the bacteria's computational and behavioral strategies are optimal given the physical constraints. In this talk, I will revisit their arguments: For the ubiquitous case of cooperatively interacting biological receptors, I will show that while cooperativity enhances the sensitivity of response to the concentration of signaling molecules, the accuracy is limited by the irreducible noise related to the random arrival of diffusing molecules. I will compare theoretical limits with quantitative experimental results for the bacterial flagellar motor demonstrating performance consistent with physical limits. I will also discuss related work focused on the bacterial chemotaxis network aimed at understanding design principles underlying properties such as robust perfect adaptation and information transmission.