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.