I will talk about how pseudospectra comes up in two different ways in my research. Firstly, I will talk the certification and computation of pseudospectra for a non-self-adjoint linear operator. Efficient calculation of the pseudospectrum for unbounded operators in infinite dimensional spaces is a relatively unexplored territory. Often finite-dimensional subspaces are used in place of the infinite dimensional space. However, the use of finite dimensional subspaces changes the qualitative nature of pseudospectral contours from unbounded curves with asymptotic behaviour at infinity to closed loops. The overlap between these curves forms the well-resolved of the pseudospectrum. It is useful to have a certification process for these calculated points. Secondly, I will talk about more recent work in using pseudospectra to model the HPA axis. Pseudospectra can be obtained via creating models or via data driven approaches. I will discuss the pros and cons of these different methods, which include interpretability and matching to experimental data.