We review some recently proposed methods to represent atomic neighbourhood environments and analyse their relative merits in terms of their faithfulness and suitability for fitting potential energy surfaces (PES). The crucial properties that such representations (commonly called descriptors) must have are continuity and invariance to the basic symmetries of physics: rotation, reflection, translation, and permutation of identical atoms. We demonstrate that schemes that initially look quite different are specific cases of a general approach, in which a finite set of basis functions with increasing angular wave numbers are used to expand the atomic neighbourhood density function. We quantitatively show using the example system of small clusters that this expansion needs to be carried to higher and higher wave numbers as the number of neighbours increases in order to obtain a faithful representation, and that variants of the descriptors converge at very different rates.