Drell–Yan lepton pair production processesare extremely important for Standard Model (SM) pre-cision tests and for beyond the SM searches at hadroncolliders. Fast and accurate predictions are essential toenable the best use of the precision measurements ofthese processes; they are used for parton density fits, forthe extraction of fundamental parameters of the SM, andfor the estimation of background processes in searches.This paper describes a new numerical program,DYTurbo,for the calculation of the QCD transverse-momentumresummation of Drell–Yan cross sections up to next-to-next-to-leading logarithmic accuracy combined withthe fixed-order results at next-to-next-to-leading order(O(α2S)), including the full kinematical dependence ofthe decaying lepton pair with the corresponding spincorrelations and the finite-width effects. TheDYTurboprogram is an improved reimplementation of theDYqT,DYResandDYNNLOprograms, which provides fast andnumerically precise predictions through the factorisationof the cross section into production and decay variables,and the usage of quadrature rules based on interpolatingfunctions for the integration over kinematic variables