I discuss the current status of the comparison between theoretical
predictions and experimental data, relevant to the production of open charm and
bottom quarks in photon-hadron and photon-photon collisions. I advocate the use
of a formalism that matches fixed-order computations to resummed computations
in order to make firm statements on heavy flavour production as described by
perturbative QCD.Comment: 10 pages Latex; 7 figures included. Talk given at EPS01, 12 - 18 July
2001, Budapest, Hungar
