I discuss how poverty decomposition methods relate to integral approximation, which is the foundation of decomposition of the temporal change of a quantity into key drivers. This offers a common framework for the different decomposition methods used in the literature, claries their often somewhat unclear theoretical underpinning and
identifes the methods'shortcomings. In light of integral approximation, many methods actually lack a sound theoretical basis and they usually have an ad-hoc character in assigning the residual terms to the different key
effects. I illustrate these claims for the Shapley-value decomposition and methods related to the Datt-Ravallion
approach and point out difficulties in axiomatic approaches to poverty decomposition. Recent developments in energy and pollutant decomposition offer some promising methods, but ultimately, further development of poverty decomposition should account for the basis in integral approximation.