Describing the behavior of low-dimensional dynamical systems usually starts with the analysis of equilibria and periodic orbits, that is, stability, instability, and bifurcations. Coherent structures such as wave trains, traveling fronts, grain bondaries, or rotating spiral waves, play an equivalent role when analyzing spatially extended dynamical systems, in particular PDEs in unbounded domains. Their analysis however brings new challenges, particularly in the form of continuous spectra for linearized operators. I will describe methods that help describe and classify coherent structures and show some curious phenomena related to the presence of continuous spectra.