  In the latter half of the last century, it became evident that there exists
an ever increasing number of different states of the so-called elementary
particles. The usual reductionist approach to this problem was to search for a
simpler infrastructure, culminating in the formulation of the quark model and
quantum chromodynamics. In a complementary, completely novel approach, Hagedorn
suggested that the mass distribution of the produced particles follows a
self-similar composition pattern, predicting an unbounded number of states of
increasing mass. He then concluded that such a growth would lead to a limiting
temperature for strongly interacting matter. We discuss the conceptual basis
for this approach, its relation to critical behavior, and its subsequent
applications in different areas of high energy physics.
