Heavy flavour production cross-sections from fixed target to collider energies

We review the hadro-production data presently available on charm and beauty absolute production cross-sections, collected by experiments at CERN, DESY and Fermilab. After correcting the published values, in particular for the 'time evolution' of the branching ratios, the measurements are compared to LO pQCD calculations performed with Pythia. as a function of the collision energy, using the latest parametrizations of the parton distribution functions. We then estimate, including nuclear effects on the parton densities, the charm and beauty production cross-sections relevant for future measurements at SPS, RHIC and LHC energies, in proton-proton and nucleus-nucleus collisions. We also compare some indirect charm measurements, done using leptonic decays, to the others and we briefly address the importance of beauty production as a feed-down mechanism of J/ psi production. (34 refs).