This review covers results on the production of all possible electroweak
boson pairs and 2-to-1 vector boson fusion at the CERN Large Hadron Collider
(LHC) in proton-proton collisions at a center of mass energy of 7 and 8 TeV.
The data were taken between 2010 and 2012. Limits on anomalous triple gauge
couplings (aTGCs) then follow. In addition, data on electroweak triple gauge
boson production and 2-to-2 vector boson scattering yield limits on anomalous
quartic gauge boson couplings (aQGCs). The LHC hosts two general purpose
experiments, ATLAS and CMS, which have both reported limits on aTGCs and aQGCs
which are herein summarized. The interpretation of these limits in terms of an
effective field theory is reviewed, and recommendations are made for testing
other types of new physics using multi-gauge boson production.Comment: 53 pages, 48 figures, 4 table