Does QCD have a Hagedorn spectrum? That is, does the number of hadrons grow
exponentially with mass for asymptotically high mass? This talk addresses the
question from both an experimental and theoretical perspective. First, it is
shown that while the data appear to be consistent with the Hagedorn conjecture,
there is surprisingly little strong evidence for it. The second part of the
talk deals with a theoretical viewpoint; in particular, we present an argument
that the large N_c limit of QCD naturally have a Hagedorn spectrum, provided
that certain technical assumptions are met.