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We discuss the theoretical bases that underpin the automation of thecomputations of tree-level and next-to-leading order cross sections, of theirmatching to parton shower simulations, and of the merging of matched samplesthat differ by light-parton multiplicities. We present a computer program,MadGraph5_aMC@NLO, capable of handling all these computations -- parton-levelfixed order, shower-matched, merged -- in a unified framework whose definingfeatures are flexibility, high level of parallelisation, and human interventionlimited to input physics quantities. We demonstrate the potential of theprogram by presenting selected phenomenological applications relevant to theLHC and to a 1-TeV $e^+e^-$ collider. While next-to-leading order results arerestricted to QCD corrections to SM processes in the first public version, weshow that from the user viewpoint no changes have to be expected in the case ofcorrections due to any given renormalisable Lagrangian, and that theimplementation of these are well under way.

The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations