In this talk I will define ‘self-similarity’ or ‘hierarchy’ for decorations of Euclidean space, with respect to a linear expansion map. Results for substitution tilings (those generated by ‘inflate, replace’ rules) can usually be extended to this broader, but very similar notion of hierarchy. In particular, we have a general recognisability result for them that drops all assumptions of minimality on their dynamical hulls. The definition applies equally well to tilings and point sets (and more). It is given in terms of basic notions from Aperiodic Order, namely of local indistinguishability and local derivability. In Symbolic Dynamics terms, the latter is essentially the idea of a sliding block code, whilst the former is of being in the same orbit closure. Many tilings are now known to be both hierarchical and projections of higher dimensional lattices, that is, constructable by the cut and project method. These include the Penrose tilings, Ammann–Beenker tilings and recently discovered hat and spectre monotilings. I will explain recent results that characterise exactly when point sets defined by Euclidean cut and project schemes are hierarchical, in terms of the cut and project data.