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I will review the GENEVA framework, that combines the NNLL resummation of large Sudakov logarithms at small values of the jet resolution variable with multiple NLO matrix-element corrections to larger values, to give a complete description at the next higher perturbative accuracy in the strong coupling constant at both small and large jet resolution scales. Recent results for several color-singlet processes, including comparison with LHC data, and extensions to handle corrections to both production and decay will also be discussed.