  A historical summary is made on the measurements concerning the rising total
hadron-hadron cross sections at high energies. The first part of this paper
concerns the total cross section measurements performed at the Brookhaven,
Serpukhov and Fermilab fixed target accelerators; then the measurements at the
CERN Intersecting Storage Rings (ISR), and at the CERN and at the Tevatron
Fermilab proton-antiproton colliders; finally the cosmic ray measurements at
even higher energies. A short discussion on Conclusions and Perspectives
follows.
