Determining the stability of solutions is an important aspect of the analysis of an applied model, because it is typically the stable solutions that are observed in practice. When studying a PDE model, several mathematical issues can arise due to the infinite dimensional nature of the problem. These include the presence of a continuous component of the spectrum and a lack of a spectral gap. An explanation of these issues will be given and techniques for overcoming them will be presented. In particular, the method of scaling variables will be introduced, which allows one to open up a gap in the spectrum and construct invariant manifolds. These manifolds can then be used to determine the nonlinear stability of the solution of interest.