  High-energy physics data analysis relies heavily on the comparison between
experimental and simulated data as stressed lately by the Higgs search at LHC
and the recent identification of a Higgs-like new boson. The first link in the
full simulation chain is the event generation both for background and for
expected signals. Nowadays event generators are based on the automatic
computation of matrix element or amplitude for each process of interest.
  Moreover, recent analysis techniques based on the matrix element likelihood
method assign probabilities for every event to belong to any of a given set of
possible processes. This method originally used for the top mass measurement,
although computing intensive, has shown its power at LHC to extract the new
boson signal from the background.
  Serving both needs, the automatic calculation of matrix element is therefore
more than ever of prime importance for particle physics. Initiated in the
eighties, the techniques have matured for the lowest order calculations
(tree-level), but become complex and CPU time consuming when higher order
calculations involving loop diagrams are necessary like for QCD processes at
LHC. New calculation techniques for next-to-leading order (NLO) have surfaced
making possible the generation of processes with many final state particles (up
to 6). If NLO calculations are in many cases under control, although not yet
fully automatic, even higher precision calculations involving processes at
2-loops or more remain a big challenge.
  After a short introduction to particle physics and to the related theoretical
framework, we will review some of the computing techniques that have been
developed to make these calculations automatic. The main available packages and
some of the most important applications for simulation and data analysis, in
particular at LHC will also be summarized.
