  We discuss the GENEVA Monte Carlo framework, which combines higher-order
resummation (NNLL) of large Sudakov logarithms with multiple
next-to-leading-order (NLO) matrix-element corrections and parton showering
(using PYTHIA8) to give a complete description at the next higher perturbative
accuracy in alpha_s at both small and large jet resolution scales. Results for
e+e- -> jets compared to LEP data and for Drell-Yan production are presented.
