Symmetries and symmetry-invariant solutions of differential equations

One of the typical applications of symmetry methods in the study of differential equations is the searching for symmetry-invariant solutions. I present here a review of and a comparison between some of the principal techniques related to this idea, including the notion of conditional symmetry (with a careful distinction between some different definitions), the concepts of partial and of $\lambda$-symmetries. The close relationship between $\lambda$-symmetries for PDE's and standard symmetries is also pointed out.