  In these lecture notes from the 2002 Cargese summer school we review the
progress that has been made towards finding a string theory for QCD (or for
pure (super)Yang-Mills theory) following the discovery of the AdS/CFT
correspondence. We start with a brief review of the AdS/CFT correspondence and
a general discussion of its application to the construction of a string theory
for QCD. We then discuss in detail two possible paths towards a QCD string
theory, one which uses a mass deformation of the N=4 super Yang-Mills theory
(the Polchinski-Strassler background) and the other using a compactification of
"little string theory" on a 2-sphere (the Maldacena-Nunez solution). A third
approach (the Klebanov-Strassler solution) is described in other lectures of
this school. We briefly assess the advantages and disadvantages of all three
approaches.
