  In this manuscript, we show how flow equation methods can be used to study
localisation in disordered quantum systems, and particularly how to use this
approach to obtain the non-equilibrium dynamical evolution of observables. We
review the formalism, based on continuous unitary transforms, and apply it to a
non-interacting yet non trivial one dimensional disordered quantum systems, the
power-law random banded matrix model whose dynamics is studied across the
localisation-delocalisation transition. We show how this method can be used to
compute quench dynamics of simple observables, demonstrate how this formalism
provides a natural framework to understand operator spreading and show how to
construct complex objects such as correlation functions. We end with an outlook
of unsolved problems and ways in which the method can be further developed in
the future. Our goal is to motivate further adoption of the flow equation
method, and to equip and encourage others to build on this technique as a means
to study localisation phenomena in disordered quantum systems.
