Bacteria are constantly sensing their environment, and must respond as it changes. Some of their most common systems for sensing and responding to change are alternative sigma factors. These are a type of transcription factor, and unique in that they integrate into the RNA polymerase molecule itself, often with dramatic effect on the bacterium’s transcriptional program. They exist in great diversity, both within and across bacterial species. Recent advances in single-cell experimental techniques have enabled studies of alternative sigma factor responses in individual cells, revealing a range of possible behaviours. These are often heterogeneous across isogenic populations, suggesting that sigma factor systems are highly noisy. In this thesis, we use stochastic modelling techniques to study what responses alterna- tive sigma factors can generate, and how these are generated. First, we present the Catalyst.jl tool for modelling chemical reaction networks. It is a useful systems biology tool that we will use to implement models of one general, and two specific (σV and σB , both in Bacillus subtilis), sigma factor circuits. Our σV model demonstrates how this circuit’s bistability properties can generate the heterogeneous activation dynamics observed experimentally. It makes additional predictions (including a memory of previous environmental conditions) that are then validated experimentally. Next, our σB model shows how this circuit’s properties enable it to generate two distinct responses, single pulse and stochastic pulsing dynamics, both previously observed in experiments. We show that, by tuning system parameters, the network can be biased towards either response behaviour, and that it can generate previously unobserved ones. Finally, we note that both the σV and the σB circuit generate their response through a mixed positive/negative feedback loop (a common alternative sigma factor circuit motif). We use this fact to build a general sigma factor model. In it, we predict a range of behaviours that these circuits should be capable of producing, including both previously observed and novel ones. We also predict how the circuit can be modulated to generate each behaviour. Our work provides detailed insight into two alternative sigma factor systems. In addition, it explains a general response mechanism these systems use, and how it can be tuned. This will be useful for synthetic biology applications, where alternative sigma factors can be used as controllers of synthetic circuits. It also reveals how bacteria can use alternative sigma factors to enable a range of strategies to respond to environmental change.