In several applications where one studies interactions mediated by a long-range kernel, it is useful to decompose this kernel into finite-range contributions, and study them separately, without losing information on the system. In my talk I present a finite-range decomposition method developed in joint work with C. Cotar for the study of multimarginal transport with interaction kernels of the type 1/|x-y|^s. This helped apply to the study of Density Functional asymptotics, decomposition techniques that extend to much higher generality, and which seem to have high potential for algorithmic applications.