Production of final states containing open charm (c) and beauty (b) quarks at HERA is reviewed. Photoproduction (PHP) of the charm meson resonancesD*,D0andDs, as well asD*production in the deep inelastic scattering (DIS) regime, are measured and compared to QCD predictions. The excited charm mesonsD10(2420),D2*0(2460)andDs1±(2536)have been observed and the rates of charm quarks hadronising to these mesons were extracted. A search for radially excited charm mesons has been performed. PHP and DIS beauty cross sections are higher than expected in next‐to‐leading order (NLO) QCD. © 2002 American Institute of Physics