The present status of the heavy-quark production theory is critically reviewed in the first contribution. The second contribution summarises the present heavy flavour data from HERA and gives an outlook of what can be expected from HERA-II. The potential of the LHC experiments for charm and beauty physics is reviewed in the 3rd contribution. Then the relevance of saturation and small-x effects to heavy quark production at HERA and at the LHC are discussed. The non-perturbative aspects of heavy-quark fragmentation and their relevance to HERA and LHC are discussed in the next contribution. Finally, a comparison of different theoretical predictions for HERA and LHC based on different approaches is presented.
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